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Unformatted text preview: MA 241 Test 1 Fall 2007 Form A -No calculators, no cell phones, no PDAs -Show all work -Begin each problem on a new page (back or front) in the blue book. Number the problems in your book. ‘ -Leave when finished My if you do not cross over someone on your row. Otherwise, wait for announcement to leave if finished about 10 minutes before the end of class. 1. Did you read the instructions? 2. Integrate (9pts) a. f x sin(4x)dx x+2 9t b. ————-dx (ps) fx2_2x_3 (9pts) c. fxe‘w‘zdx X e 1+e" (9pts) d. f 3. Given f xxi x4 ~16 dx and the 4 formulas from the tables: 2 l. fw/uZ—a2 du-gwiuz—az—%lnu+Vu2—a2|+c 4 II. fuZVuz—azdu=€-(2u2 —a2)'\/u2 -a2 -%lniu+‘\/u2 —a2 +c 2 III. f‘Jaz—uzduugw/az-uz+%sin"£+c a 4 IV- 1131/02 - uzdu = %(2u2 — 051/02 — u2 + %sin"£+ c a (3pts) a, Clearly state u, a, and du. (lpt) b. Which formula (I, II, III or IV) is used to integrate this problem. (4pts) c. Using the formula, integrate. 2 x 4. (8pts) Approximate .(i). 75'“ using Simpson’s Rule with n=4 subintervals. Do not 6 simplify the arithmetic. CONTINUE ON NEXT PAGE 5. Improper Integrals 1 co (8pts) a. Determine if I] de is convergent or divergent. If it is convergent, evaluate. (Spts) b. If f (x) 2 g(x) 2 0 and if I: f converges, what does the Comparison Theorem tell you about I :0 8(x)dx , if anything. 6. Given the region bounded by y = y = 0, and y = 6 - x, set up the definite integral with all appropriate numbers but do not evaluate to find (3pts) a. Make a good sketch and shade the bounded region (8pts) b. The area of the bounded region. 0. The volume of the solid generated by revolving the region about (8pts) 1’. x — axis (8pts) ii. x =10 3 7. (8pts) Find the length of the curve x = ya, 0 s y s l. S I , . C ; . . l. I- /d 1T 5. 1r ,\, U 4 H, .. a . I , , .. a x . a W g X . . _. fl 5 1 I. L s 1 u ’ , . yr. «LI... 7 r y , x i H 5 , , . , , D. I o ‘ _ [(U i 3 M r v« Z L X/ Vr’ L _ ,WM vf X g L! U; e e ’ VA, (J . ...
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This note was uploaded on 03/20/2008 for the course MA 141 and 24 taught by Professor Dempster/mccolum during the Spring '08 term at N.C. State.

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