Explanation Given Information: The provided function is ∫ ( x − 1 ) sin ( x 2 − 2 x + 1 ) d x . Formula Used: If u is a function of x, then the rule to evaluate an integral is ∫ f d x = ∫ ( f d u / d x ) d u where d u d x a derivative of the function with respect to x and solve for d x in terms of d u . Constant multiple rules is ∫ k ⋅ g ( x ) d x = k ∫ g ( x ) d x where k is a constant. If the function is f ( x ) = sin ( a x ) , then the formula for the integration of the function is given by ∫ sin ( a x ) d x = − 1 a cos ( a x ) + C . Calculation: Consider the function ∫ ( x − 1 ) sin ( x 2 − 2 x + 1 ) d x . Replace the parenthetical expression with variable u . u = x 2 − 2 x + 1 Determine the derivative of u with respect to x , d u d x = d d x x 2 − 2 x + 1 d u d x = 2 x − 2 Determine the value of d x , d x = 1 2 ( x − 1 ) d u Substitute the value of d x into the integral

7th Edition

ISBN: 9781337514309

Author: Waner

Publisher: Cengage

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Chapter 9, Problem 16RE

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To calculate: The integral of the function ∫(x−1)sin(x2−2x+1)dx.

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Chapter 9, Problem 15RE

Chapter 9, Problem 17RE

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Chapter 9 Solutions

Applied Calculus

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The integral of the function ∫ ( x − 1 ) sin ( x 2 − 2 x + 1 ) d x .

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To calculate: The integral of the function ∫(x−1)sin(x2−2x+1)dx.

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Chapter 9 Solutions