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20b_01w_2e - Math 20B Second Exam(125 points 4:40 PM March...

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Math 20B Second Exam (125 points) 4:40 PM March 5, 2001 Please put your name, ID number, and section number (or time) on your blue book. The exam is CLOSED BOOK, but you may use ONE SHEET OF NOTES. Calculators are NOT allowed. You must show your work to receive credit. 1. (80 pts.) Evaluate the following integrals. Remember to show your work! (a) Z 1 / 2 0 x 1 - x 2 dx (b) Z t t + 3 t · dt (c) Z sin 2 t cos 3 t dt (d) Z (ln x ) 2 dx (e) Z 1 - 1 1 x 3 dx 2. (15 pts.) Set up the integral for the volume of the solid obtained by rotating the region bounded by y = 0 , y = sin x, 0 x π about the line y = 1. Your answer should include a sketch of the region together with the line about which the region is being rotated.
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