MA 126 Midterm: 2-12s-test3

Instructions: You may work with other students, but be sure to write up an individual solution and list everyone you worked with. Note: I ask that you do not explicitly compute the area/volume, just write down the integral. However, I have given answers so you can check your solution if you wish. There are various online resources for computing integrals, which you may use to check your answer. I need to see your work! If I see a paper with just a list of integrals, it will not receive full credit. Set up an integral (or sum of integrals) which gives the area of the region enclosed by the given curves. y = 4x2, y = x2, y = 16. (Ans: 128/3) First do it with respect to y, then do it with respect to x. Which method did you find superior? Set up an integral which gives the volume of the solid obtained by rotating the region bounded by the given curves about the specificed line. Use the method of cylindrical shells to set up an integral which gives the volume of the solid generated by rotating the region bounded by x + y = 3 and x - 4 - (y - l)2 about the x-axis. (Ans: 27pi/2)

Instructions: You may work with other students, but be sure to write up an individual solution and list everyone you worked with. Note: I ask that you do not explicitly compute the area/volume, just write down the integral. However, I have given answers so you can check your solution if you wish. There are various online resources for computing integrals, which you may use to check your answer. I need to see your work! If I see a paper with just a list of integrals, it will not receive full credit. Set up an integral (or sum of integrals) which gives the area of the region enclosed by the given curves. y = sin(pix/2), y = x2 - 2x (Ans: 4/3 + 4/pi) y = 4x2, y = x2, y = 16. (Ans: 128/3) First do it with respect to y, then do it with respect to x. Which method did you find superior? Set up an integral which gives the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. x = y - y2, x = 0; about the y-axis (Ans: pi/30) y = sin x, y = cos x, 0 x pi/4; about y = - 1 (Ans: ( -3/2)pi) y = x, y = 0, x = 2, x = 4; about x = 1 (Ans: 76 pi/3) Use the method of cylindrical shells to set up an integral which gives the volume of the solid generated by rotating the region bounded by x + y = 3 and x = 4 - (y - 1)2 about the x-axis. (Ans: 27pi/2)