Stewart - Calculus ET 8e Chapter 15. All Answers

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1. Calculate the iterated integral. 2. Evaluate where is the figure bounded by and . 3. Evaluate the integral by changing to polar coordinates. is the region bounded by the semicircle and the -axis... . 4. Describe the region whose area is given by the integral. 5. Find the mass of the lamina that occupies the region and has the given density function. Round your answer to two decimal places. 6. Find the area of the surface. The part of the surface that lies within the cylinder . 7. Use spherical coordinate to find the volume above the cone and inside sphere . 8. Calculate the iterated integral. 9. Find the volume of the solid bounded in the first octanat bounded by the cylinder and the planes .Stewart - Calculus ET 8e Chapter 15 Form A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 10. Calculate the iterated integral. 11. Determine whether to use polar coordinates or rectangular coordinates to evaluate the integral , where f is a continuous function. Then write an expression for the (iterated) integral. –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 x 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 y 12. Evaluate the integral , where R is the annular region bounded by the circles and by changing to polar coordinates. 13. Find the center of mass of the lamina of the region shown if the density of the circular lamina is four times that of the rectangular lamina. –2 2 x 1 –1 y 14. Find the mass and the center of mass of the lamina occupying the region R, where R is the region bounded by the graphs of and and having the mass densityStewart - Calculus ET 8e Chapter 15 Form A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 15. Find the mass and the moments of inertia and and the radii of gyration and for the lamina occupying the region R, where R is the region bounded by the graphs of the equations and and having the mass density 16. Find the area of the surface S where S is the part of the plane that lies above the triangular region with vertices , and 17. Find the area of the surface S where S is the part of the sphere that lies inside the cylinder 18. Sketch the solid bounded by the graphs of the equations and , and then use a triple integral to find the volume of the solid. 19. Sketch the solid whose volume is given by the iterated integral 20. Find the center of mass of a homogeneous solid bounded by the paraboloid andStewart - Calculus ET 8e Chapter 15 Form A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer Key 1. 2. 14 3. 4. half the region inside the loop of the four-leaved in quadrant I and IV 5. 6. 7. 8. 9. 18 10. 11. Polar, 12. 7 2 13. 14. , 15. 64 5 , 16, 144 5 , 3 16. 17.Stewart - Calculus ET 8e Chapter 15 Form A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 18. 19. 20.Stewart – Calculus ET 8e Chapter 15 Form B © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1. Calculate the double integral. Round your answer to two decimal places. 2. Calculate the double integral. Round your answer to two decimal places. 3. Calculate the iterated integral. 4. Evaluate the integral by reversing the order of integration. 5. An agricultural sprinkler distributes water in a circular pattern of radius ft. It supplies water to a depth of feet per hour at a distance of feet from the sprinkler. What is the total amount of water supplied per hour to the region inside the circle of radius feet centered at the sprinkler? 6. Use polar coordinates to evaluate. 7. Evaluate the triple integral. Round your answer to one decimal place. lies under the plane and above the region in the -plane bounded by the curves , and . 8. Use spherical coordinate to find the volume above the cone and inside sphere .Stewart – Calculus ET 8e Chapter 15 Form B © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 9. Evaluate the integral by making an appropriate change of variables. Round your answer to two decimal places. R is the parallelogram bounded by the lines . 10. Find the volume of the solid bounded in the first octanat bounded by the cylinder and the planes . 11. Evaluate the double integral , where 12. Evaluate the double integral , where is the region bounded by the graphs of and . 13. Determine whether to use polar coordinates or rectangular coordinates to evaluate the integral , where f is a continuous function. Then write an expression for the (iterated) integral. –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 x 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 y 14. Find the center of mass of the system comprising masses mk located at the points Pk in a coordinate plane. Assume that mass is measured in grams and distance is measured in centimeters. m1 = 4, m2 = 3, m3 = 1 P1(3, –3), P2(5, –1), P3(2, –5)Stewart – Calculus ET 8e Chapter 15 Form B © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 15. Find the mass and the center of mass of the lamina occupying the region R, where R is the region bounded by the graphs of and and having the mass density 16. Find the area of the surface S where S is the part of the surface that lies inside the cylinder 17. Find the area of the surface S where S is the part of the sphere that lies to the right of the xz-plane and inside the cylinder 18. Sketch the solid bounded by the graphs of the equations and , and then use a triple integral to find the volume of the solid. 19. Identify the surface with equation 20. Identify the surface with equationStewart – Calculus ET 8e Chapter 15 Form B © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer Key 1. 2. 3. 4. 5. 6. 7. 8. 9. 0.28 10. 18 11. 22 12. 189 20 13. Polar, 14. 15. , 16. 17.Stewart – Calculus ET 8e Chapter 15 Form B © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 18. 19. Upper half of a right circular cone with vertex the origin and axis the positive z-axis 20. Sphere with radius 7 centered at the originStewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Select the correct answer for each question. ____ 1. Evaluate the double integral by first identifying it as the volume of a solid. a. b. c. d. e. ____ 2. Use the Midpoint Rule with four squares of equal size to estimate the double integral. a. b. c. d. e. ____ 3. Calculate the double integral. a. b. c. d. e. ____ 4. Use polar coordinates to find the volume of the solid under the paraboloid and above the disk . a. b. c. d. e.Stewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 5. Evaluate the iterated integral by converting to polar coordinates. Round the answer to two decimal places. . a. b. c. d. e. ____ 6. A swimming pool is circular with a -ft diameter. The depth is constant along east-west lines and increases linearly from ft at the south end to ft at the north end. Find the volume of water in the pool. a. b. c. d. e. ____ 7. Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. Assume the vertex opposite the hypotenuse is located at , and that the sides are along the positive axes. a. b. c. d. e. None of theseStewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 8. Find the area of the surface. The part of the surface that lies above the xy-plane. a. b. 2 75 c. 2 75 d. 2 75 e. ____ 9. Calculate the iterated integral. a. 8 3 b. 4 c. d. e. None of theseStewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 10. Use a triple integral to find the volume of the solid bounded by and the planes and . a. b. c. d. e. ____ 11. Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and a. 8 3 b. 4 c. 32 d. 48 ____ 12. Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane . a. 8.57 b. 0 c. 3.4 d. 9.19 e. 0.54 ____ 13. Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate where E lies above the paraboloid and below the plane . a. 160.28 b. 176.38 c. d. 175.93 e. 175.37Stewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 14. Use spherical coordinates. Evaluate , where is the ball with center the origin and radius . a. b. c. d. e. None of these ____ 15. Use spherical coordinates to evaluate where B is the ball a. 10000 b. 10 c. 1000 d. 2000Stewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 16. The sketch of the solid is given below. Given , write the inequalities that describe it. a. b. None of these c. d. e. ____ 17. Find the Jacobian of the transformation. a. b. c. d. e.Stewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 18. Use the transformation to evaluate the integral , where R is the region bounded by the ellipse . a. b. c. d. e. ____ 19. Calculate the iterated integral. a. b. c. d. e.Stewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 20. Evaluate the iterated integral. a. b. c. d. e.Stewart - Calculus ET 8e Chapter 15 Form C © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer Key 1. E 2. C 3. E 4. E 5. A 6. E 7. A 8. C 9. A 10. A 11. A 12. B 13. C 14. A 15. A 16. D 17. C 18. E 19. E 20. AStewart - Calculus ET 8e Chapter 15 Form D © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Select the correct answer for each question. ____ 1. Evaluate the double integral by first identifying it as the volume of a solid. a. b. c. d. e. ____ 2. Find the volume of the solid bounded by the surface and the planes and coordinate planes. a. b. c. d. e. ____ 3. Calculate the double integral. a. b. c. d. e. ____ 4. Use polar coordinates to find the volume of the solid under the paraboloid and above the disk . a. b. c. d. e.Stewart - Calculus ET 8e Chapter 15 Form D © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 5. Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . a. b. c. d. e. ____ 6. Use polar coordinates to find the volume of the solid inside the cylinder and the ellipsoid . a. b. c. d. e. ____ 7. Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and , and having the mass density a. , b. 10, c. 10, d. ,Stewart - Calculus ET 8e Chapter 15 Form D © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 8. An electric charge is spread over a rectangular region Find the total charge on R if the charge density at a point in R (measured in coulombs per square meter) is a. 84 coulombs b. 222 coulombs c. 22 coulombs d. 56 coulombs ____ 9. Find the center of mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the x-axis. a. b. c. d. e. None of these ____ 10. Find the area of the part of hyperbolic paraboloid that lies between the cylinders and . a. b. c. 1 9 d. 1 9 e. 1 9Stewart - Calculus ET 8e Chapter 15 Form D © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 11. Calculate the iterated integral. a. 8 3 b. 4 c. d. e. None of these ____ 12. Use a triple integral to find the volume of the solid bounded by and the planes and . a. b. c. d. e. ____ 13. Evaluate the integral where and with respect to x, y, and z, in that order. a. 28 b. 36 c. 4 d. 24Stewart - Calculus ET 8e Chapter 15 Form D © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 14. Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and a. 4 b. 8 3 c. 24 d. 16 ____ 15. Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane . a. 8.57 b. 0 c. 3.4 d. 9.19 e. 0.54 ____ 16. Use spherical coordinates. Evaluate , where is the ball with center the origin and radius . a. b. c. d. e. None of theseStewart - Calculus ET 8e Chapter 15 Form D © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 17. Use the given transformation to evaluate the integral. , where R is the region in the first quadrant bounded by the lines and the hyperbolas . a. 9.447 b. 3.296 c. 8.841 d. 4.447 e. 5.088 ____ 18. Evaluate the iterated integral. a. b. c. d. e. ____ 19. Use a computer algebra system to find the moment of inertia of the lamina that occupies the region D and has the density function , if . a. 14.1 b. 34.138 c. 24.105 d. 28.5 e. None of these ____ 20. Calculate the iterated integral. Round your answer to two decimal places. a. b. c. d. e.Stewart - Calculus ET 8e Chapter 15 Form D © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer Key 1. A 2. D 3. D 4. C 5. C 6. E 7. D 8. A 9. C 10. E 11. A 12. A 13. C 14. B 15. B 16. B 17. B 18. B 19. A 20. EStewart - Calculus ET 8e Chapter 15 Form E © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1. Find the volume under and above the region bounded by and . ____ 2. Find the volume of the solid bounded by the surface and the planes and coordinate planes. Select the correct answer. a. b. c. d. e. 3. Calculate the double integral. 4. Evaluate the iterated integral by converting to polar coordinates. Round the answer to two decimal places. . 5. Use polar coordinates to find the volume of the solid inside the cylinder and the ellipsoid .Stewart - Calculus ET 8e Chapter 15 Form E © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 6. Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and , and having the mass density Select the correct answer. a. 25, b. , c. 25, d. , 7. Find the area of the part of hyperbolic paraboloid that lies between the cylinders and . ____ 8. Find the area of the part of the sphere that lies inside the paraboloid . Select the correct answer. a. b. c. d. e. 9. Find the area of the surface. The part of the sphere that lies above the plane . 10. Calculate the iterated integral.Stewart - Calculus ET 8e Chapter 15 Form E © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 11. Use a triple integral to find the volume of the solid bounded by and the planes and . Select the correct answer. a. b. c. d. e. 12. Evaluate where and T is the region bounded by the paraboloid and the plane ____ 13. Use cylindrical coordinates to evaluate Select the correct answer. a. 12 b. 112 c. 3 2 d. 14 14. Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane . 15. Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate where E lies above the paraboloid and below the plane .Stewart - Calculus ET 8e Chapter 15 Form E © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 16. Use spherical coordinates to evaluate where B is the ball Select the correct answer. a. 2401 b. 343 c. 686 d. 7 17. Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is directly proportional to its distance from the base of the solid. ____ 18. Use the given transformation to evaluate the integral. , where R is the region in the first quadrant bounded by the lines and the hyperbolas . Select the correct answer. a. 9.447 b. 3.296 c. 8.841 d. 4.447 e. 5.088 19. Evaluate the iterated integral. 20. Calculate the iterated integral. Round your answer to two decimal places.Stewart - Calculus ET 8e Chapter 15 Form E © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer Key 1. 3 13 2. D 3. 4. 5. 6. B 7. 2 9 8. B 9. 10. 8 3 11. A 12. 7 3 13. D 14. 0 15. 16. A 17. 625 4 k 18. B 19. 20.Stewart – Calculus ET 8e Chapter 15 Form F © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 1. Evaluate the double integral by first identifying it as the volume of a solid. Select the correct answer. a. b. c. d. e. 2. Use the Midpoint Rule with four squares of equal size to estimate the double integral. 3. Estimate the volume of the solid that lies above the square and below the elliptic paraboloid . Divide into four equal squares and use the Midpoint rule. 4. Find the volume of the solid bounded by the surface and the planes and coordinate planes. ____ 5. Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . Select the correct answer. a. b. c. d. e. 6. Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and , and having the mass densityStewart – Calculus ET 8e Chapter 15 Form F © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 7. Find the center of mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the x-axis. ____ 8. Find the mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the line . Select the correct answer. a. 45 2 b. 5 2 c. 45 d. 3 e. None of these 9. Find the area of the surface. The part of the surface that lies above the xy-plane. 10. Find the area of the surface. The part of the sphere that lies above the plane . 11. Calculate the iterated integral.Stewart – Calculus ET 8e Chapter 15 Form F © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 12. Use a triple integral to find the volume of the solid bounded by and the planes and . Select the correct answer. a. b. c. d. e. 13. Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3. ____ 14. Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane . Select the correct answer. a. 8.57 b. 0 c. 3.4 d. 9.19 e. 0.54 15. Use cylindrical coordinates to evaluate where E is the region that lies inside the cylinder and between the planes . Round the answer to two decimal places. 16. Use spherical coordinates to evaluate where B is the ballStewart – Calculus ET 8e Chapter 15 Form F © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 17. The sketch of the solid is given below. Given , write the inequalities that describe it. 18. Calculate the iterated integral. ____ 19. Evaluate the iterated integral. Select the correct answer. a. b. c. d. e. 20. Use a computer algebra system to find the moment of inertia of the lamina that occupies the region D and has the density function , if .Stewart – Calculus ET 8e Chapter 15 Form F © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer Key 1. E 2. 3. 4. 5. C 6. , 7. 8. A 9. 1 54 10. 11. 16 3 12. A 13. 19.63 14. B 15. 16. 1296 17. 18. 19. A 20. 14.1Stewart – Calculus ET 8e Chapter 15 Form G © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 1. Calculate the double integral. Select the correct answer. a. b. c. d. e. 2. Use polar coordinates to find the volume of the solid under the paraboloid and above the disk . 3. Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane . 4. Use a double integral to find the area of the region R where R is bounded by the circle ____ 5. An electric charge is spread over a rectangular region Find the total charge on R if the charge density at a point in R (measured in coulombs per square meter) is Select the correct answer. a. 804 coulombs b. 91 coulombs c. 300 coulombs d. 265 coulombs 6. Find the center of mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the x-axis.Stewart – Calculus ET 8e Chapter 15 Form G © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 7. Find the mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the line . Select the correct answer. a. 3 2 b. 2 c. 27 d. 27 2 e. None of these 8. Find the area of the part of hyperbolic paraboloid that lies between the cylinders and . 9. Find the area of the surface. Round your answer to three decimal places. 10. Find the area of the part of the sphere that lies inside the paraboloid . 11. Calculate the iterated integral.Stewart – Calculus ET 8e Chapter 15 Form G © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 12. Evaluate the integral where and with respect to x, y, and z, in that order. Select the correct answer. a. 4 b. 28 c. 36 d. 24 ____ 13. Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3. Select the correct answer. a. 16.25 b. 15.07 c. 24.91 d. 13.92 e. 19.63 14. Use cylindrical coordinates to evaluate 15. Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane . ____ 16. Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius and density 1 about a diameter of its base. Select the correct answer. a. 205.13 b. c. 195.22 d. 213.5 e. 198.08Stewart – Calculus ET 8e Chapter 15 Form G © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 17. Find the Jacobian of the transformation. 18. Use the transformation to evaluate the integral , where R is the region bounded by the ellipse . 19. Use the given transformation to evaluate the integral. , where R is the region in the first quadrant bounded by the lines and the hyperbolas . ____ 20. Evaluate the iterated integral. Select the correct answer. a. b. c. d. e.Stewart – Calculus ET 8e Chapter 15 Form G © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer Key 1. B 2. 3. 4. 32 5. A 6. 7. D 8. 2 9 9. 10. 11. 8 3 12. A 13. E 14. 14 15. 0 16. B 17. 18. 19. 3.296 20. AStewart - Calculus ET 8e Chapter 15 Form H © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 1. Evaluate the double integral by first identifying it as the volume of a solid. Select the correct answer. a. b. c. d. e. 2. Estimate the volume of the solid that lies above the square and below the elliptic paraboloid . Divide into four equal squares and use the Midpoint rule. ____ 3. Use polar coordinates to find the volume of the solid under the paraboloid and above the disk . Select the correct answer. a. b. c. d. e. ____ 4. Use a double integral to find the area of the region R where R is bounded by the circle Select the correct answer. a. 64 b. 16 c. 8 d. 32 5. Use polar coordinates to find the volume of the sphere of radius . Round to two decimal places.Stewart - Calculus ET 8e Chapter 15 Form H © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 6. For which of the following regions would you use rectangular coordinates? a. c. b. 7. Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. Assume the vertex opposite the hypotenuse is located at , and that the sides are along the positive axes. 8. Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and , and having the mass density 9. Find the mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the line . ____ 10. Find the area of the part of the sphere that lies inside the paraboloid . Select the correct answer. a. b. c.Stewart - Calculus ET 8e Chapter 15 Form H © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. d. e. 11. Find the area of the surface. The part of the sphere that lies above the plane . ____ 12. Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3. Select the correct answer. a. 16.25 b. 15.07 c. 24.91 d. 13.92 e. 19.63 13. Evaluate where and T is the region bounded by the paraboloid and the plane 14. Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane . 15. Use cylindrical coordinates to evaluate where E is the region that lies inside the cylinder and between the planes . Round the answer to two decimal places.Stewart - Calculus ET 8e Chapter 15 Form H © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ____ 16. The sketch of the solid is given below. Given , write the inequalities that describe it. Select the correct answer. a. None of these b. c. d. e. 17. Find the Jacobian of the transformation. 18. Use the given transformation to evaluate the integral. , where R is the region in the first quadrant bounded by the lines and the hyperbolas . 19. Use the given transformation to evaluate the integral. , where R is the square with vertices (0, 0), (4, 6), (6, ), (10, 2) and 20. Calculate the iterated integral.Stewart - Calculus ET 8e Chapter 15 Form H © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer Key 1. C 2. 3. E 4. D 5. 6. A 7. 8. , 9. 27 2 10. B 11. 12. E 13. 7 3 14. 0 15. 16. E 17. 18. 3.296 19. 312 20. [Show More]

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