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Math 1210 Quiz 10 April 11th, 2014 Answer the following 2 questions. The value of every question is indicated at the beginning of it. You may use scratch paper, but you can only turn in this sheet. Please write your answer in the space provided. You have 20 minutes. Name: UID: 1. (14 points) Let R be the region in the first quadrant bounded by the graphs of y = x = 4 and y = 0. √ x, (i) Write down the integral that would compute the volume of the solid obtained by revolving R about the x-axis. (a) (5 points) Using shells: Solution: 2 Z 2πy(4 − y 2 ) dy V = 0 (b) (5 points) Using disks: Solution: Z 4 π V = √ 2 x dx 0 (ii) (4 points) Use any method to write down the integral that would compute the volume of the solid obtained by revolving R about the line x = −1. Solution: Using disks we get Z 4 V = √ π ( x + 1)2 − 12 dx 0 Using shells the integral would be Z 2 V = 2π(y + 1)(4 − y 2 ) dy 0 2. (16 points) Let R be the region in the first quadrant bounded by the graphs of y = x2 and y = 2 − x2 . Write down the integral that would compute the volume of the solid obtained by revolving R about the y-axis. (i) (8 points) Using shells: Solution: Z V = 1 4πx(1 − x2 ) dx 0 (ii) (8 points) Using disks: Solution: Z 1 Z 1 0 Page 2 2 π(2 − y) dy πy dy + V =