You must show your work to obtain full credit. Points may be deducted if you do not justify your nal answer. Please indicate clearly whenever you continue your work on the back of the page. The exam is worth a total of 200 points. 1: (10 points each) evaluate the following integrals. (a) z x2e3x dx (b) z. 8x 11 x2 3x + 2 dx (continued on the next page. ) 2 (continued from the previous page. ) (c) z x2. 4: (20 points) let r be the region bounded by y = x2, x = 1, and y = 0, and let s be the solid of revolution obtained by revolving r about the line x = 2. The bowl is lled with water to a height of y = 9 m. Set up, but do not evaluate, an integral which gives the work required to pump all of the water to the top of the bowl (y = 16 m).
