MATH
section8_5

# section8_5 - The first step in evaluating 9x x dx is 2 x 9...

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The first step in evaluating is …. a) Partial fraction decomposition b) A substitution c) Algebraic manipulation d) Integration by parts 9 x + x 3 x 2 + 9 ! dx e) Long division

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The first step in evaluating is algebraic manipulation. 9 x + x 3 x 2 + 9 ! dx 9 x + x 3 x 2 + 9 = x (9 + x 2 ) x 2 + 9 = x ! 9 x + x 3 x 2 + 9 " dx = x " dx = x 2 2 + C
The first step in evaluating is …. a) Partial fraction decomposition b) A substitution c) Completing the square in the denominator d) Integration by parts x 9 + x 4 ! dx e) Long division

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The first step in evaluating is substitution. The best substitution is: a) u=x b) u=x 4 c) u=9+x 4 d) None of the above. x 9 + x 4 ! dx
The best substitution to evaluate is u=x 2 x 9 + x 4 ! dx u = x 2 , du = 2 xdx ! x 9 + x 4 " dx = 1 2 1 9 + u 2 " du = 1 2 1 9 1 1 + ( u 2 / 9) " du = = 1 18 1 1 + ( u / 3) 2 " du = 1 18 3tan # 1 u 3 \$ % & ( ) + C = 1 6 tan # 1 x 2 3 \$ % & ( ) + C

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The first step in evaluating is …. a) Partial fraction decomposition b) A substitution c) Algebraic manipulation d) Integration by parts 9 + x 3 x 4 !
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