Mathematics > QUESTIONS & ANSWERS > University of Maryland, College ParkMATH 141 GSS PROBLEM SET (I & II) SOLUTIONS (All)

University of Maryland, College ParkMATH 141 GSS PROBLEM SET (I & II) SOLUTIONS

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MATH-141 GUIDED STUDY SESSIONS PROBLEM SET-I (APPLICATIONS OF INTEGRATION) (Computing Volume Using Disc, Washer, and Shell Methods) Question-I: Find the volume of the solid obtained by rotating th... e region bounded by ? = ?3, ? = 8, and ? = 0 about the y-axis using Disc Method. Question-II: Let R be the region between the graphs of ?(?) = cos(?) + sin(?), and ?(?) = cos(?) − sin(?) on the interval [0, ? 4 ]. Find the volume V of the solid obtained by revolving R about the x-axis using Washer Method. Question-III: Use the method of cylindrical shells (Shell Method) to find the volume of the solid obtained by rotating the region enclosed by the given curves about the x-axis. (a) ? + ? = 3, ? = 4 − (? − 1)2. (b) ? = ?3, ? = 8, ? = 0. (c) ? = √? , ? = 0, ? = 2. Question-IV: Find the volume of the solid obtained by rotating the region bounded by ? = ? − ?2 and ? = 0 about the line ? = 2. Question-V: Find the volume of the solid obtained by rotating the region R enclosed by the curves ? = ? and ? = ?2 about the line ? = −1 using Washer Method. Question-V1: Let R be the region between the graphs of ?(?) = 1 (?+2)2 and ?(?) = (?+1 2) on the interval [0,2]. Use the Shell Method to find the volume V of the solid obtained by revolving R about the x-axis.MATH-141 GUIDED STUDY SESSIONS PROBLEM SET-II SOLUTIONS (APPLICATIONS OF INTEGRATION) (Work: Spring and Tank Problems) Question-I: A spring has a natural length of 2ft. and a force of 15 lbs. is required to hold it compressed at a length of 18in. How much work is done in stretching the spring from its natural length to a length of 3ft.? [Show More]

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