quiz4_sol_1

quiz4_sol_1 - Math 118 39439 Quiz 4 November 13 Fall 2008...

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Unformatted text preview: Math 118: 39439, Quiz 4, November, 13, Fall 2008, Name: : . Discussion : PROBLEM 1 (3 pts) Find the antiderivatives Substitute u = x2 + 1, du = 2xdx, x2 2x dx = +1 2x dx x2 +1 du = ln |u| + C = ln |x2 + 1| + C. u PROBLEM 2 (3 pts) Find the antiderivatives x(x + 1)8 dx. Integrate by parts g = (x + 1)8 , f = x, x(x + 1)8 dx = (x + 1)9 x- 9 (x + 1)9 (x + 1)9 (x + 1)10 1dx = x- + C. 9 9 90 PROBLEM 3 (4 pts) Find the antiderivatives x3 ex dx. Integrate by parts three times, rst g = ex , f = x3 , then f = x2 , then f = x x3 ex dx = x3 ex - 3 x2 ex dx xex dx xex dx ex dx = x3 ex - 3 x2 ex dx - 2 = x3 ex - 3x2 ex dx + 6 = x3 ex - 3x2 ex dx + 6 xex - = x3 ex - 3x2 ex dx + 6xex - 6ex + C. End. ...
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This note was uploaded on 06/26/2009 for the course MATH 118x taught by Professor Vorel during the Fall '07 term at USC.

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