Quiz 8 Solution

Quiz 8 Solution - MATH 1142 Quiz 8A Solutions Nathan T Gray...

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MATH 1142: Quiz 8A Solutions Nathan T. Gray Fall 2013 Exercise 1. Evaluate ° 2 x +1 x 2 + x +3 dx. Solution. Let u = x 2 + x ,d u =(2 x + 1) dx. Then ° 2 x x 2 + x dx = ° 1 u du = ° u 1 / 2 du = u 1 / 2 1 / 2 + C = 2( x 2 + x + 3) 1 / 2 + C, or equivalently, ° 2 x x 2 + x dx =2 ± x 2 + x +3+ C. Exercise 2. Evaluate ² x 4 x 2 dx . Solution. Let u =4 x 2 u = 2 xdx, 1 2 du = xdx. Then ° x ± 4 x 2 dx = ° u · ( 1 2 ) du = 1 2 ° u 1 / 2 du = 1 3 u 3 / 2 + C = 1 3 (4 x 2 ) 3 / 2 + C. Exercise 3. Evaluate ² 2 0 4 x (1 + x 2 ) 3 dx . Solution. Let u =1+ x 2 u 2 du If x = 0, then u =1+0 2 = 1. If x = 2, then u =1+2 2 = 5. Then ° 2 0 4 x (1 + x 2 ) 3 dx = ° 5 1 2 u 3 du = 1 2 u 4 ³ ³ ³ 5 1 = 1 2 (5 4 1) = 312 .

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MATH 1142: Quiz 8B Solutions Nathan T. Gray Fall 2013 Exercise 1. Evaluate ° 2 x ( x 2 + 4) 5 dx . Solution. Let u = x 2 +4 ,d u =2 xdx. Then ± 2 x ( x 2 + 4) 5 dx = ± u 5 du = 1 6 u 6 + C = 1 6 ( x 2 + 4) 6 + C. Exercise 2. Evaluate ± 1 2 x +1 dx. Solution. Let u x u dx, 1 2 du = dx. Then ± 1 2 x dx = ± 1 u ·
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Quiz 8 Solution - MATH 1142 Quiz 8A Solutions Nathan T Gray...

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