quiz3sol - Quiz Solutions 1. Evaluate the following...

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Unformatted text preview: Quiz Solutions 1. Evaluate the following indefinite integral: x3 dx x2 - 1 Solution: x3 dx = x2 - 1 x dx + x dx -1 x2 1 2 x + 2 1 = x2 + 2 = 1 du ; u = ln(x2 - 1) 2 u 1 ln(x2 - 1) + C 2 2. Evaluate the following indefinite integral: ln x dx (x + 1)3 Solution: Take u = ln x, du = dx x , dv = dx (x+1)3 , v 1 = - 2(x+1)2 . ln x ln x 1 dx = - + 3 2 (x + 1) 2(x + 1) 2 dx x(x + 1)2 1 A B C = + + 2 x(x + 1) x x + 1) (x + 1)2 1 A= |x=0 = 1 (x + 1)2 1 C = |x=-1 = -1 x 1 B = - 2 |x=-1 = -1 x ln x ln x 1 1 1 1 =- + ( - - )dx (x + 1)3 2(x + 1)2 2 x x + 1 (x + 1)2 1 ln x 1 1 1 =- + ln x - ln(x + 1) + +C 2 (x + 1)2 2 2 2(x + 1) 3. Evaluate the following definite integral: 212 26 dx x- 3x 1 2 Solution: Take u6 = x, 6u5du = dx. 212 26 dx =6 x- 3x =6 4 2 4 2 4 u5 du u3 - u2 = 160 + 6 ln 3 = 128 + 48 + 24 + 6 ln(3) - 16 - 12 - 12 1 du u-1 2 = 6[1/3u3 + 1/2u2 + u + ln(u - 1)]|4 2 =6 u2 + u + 1 + u3 du u-1 ...
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This note was uploaded on 11/23/2010 for the course CIVIL 105 taught by Professor No during the Spring '10 term at Lovely Professional University.

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quiz3sol - Quiz Solutions 1. Evaluate the following...

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