Explanation Given information: The integral function is ∫ 0 t e s sin ( t − s ) d s . Calculation: Show the equation of the curve as follows: ∫ 0 t e s sin ( t − s ) d s (1) Show the method of integration by parts as shown below: ∫ u d v = u v − ∫ v d u (2) Consider u = sin ( t − s ) Differentiate both sides of the Equation. d u = − cos ( t − s ) d s Consider d v = e s d s Integrate both sides of the Equation. v = e s Apply method of integration by parts in Equation (1) as shown below. Substitute sin ( t − s ) for u , − cos ( t − s ) d s for du , e s for v , and e s d s for dv in Equation (2). ∫ e s sin ( t − s ) d s = sin ( t − s ) e s − ∫ e s ( − cos ( t − s ) ) d s = e s sin ( t − s ) + ∫ e s cos ( t − s ) d s (3) Consider u = cos ( t − s ) Differentiate both sides of the Equation. d u = sin ( t − s ) d s Consider d v = e s d s Integrate both sides of the Equation. v = e s Substitute cos ( t − s ) for u , sin ( t − s ) d s for du , e s for v , and e s d s for dv in Equation (2)

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ISBN: 9781337772020

Author: Stewart

Publisher: VST

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Chapter 6.1, Problem 26E

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To calculate: The value of the integral function ∫0tessin(t−s) ds.

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Chapter 6.1, Problem 25E

Chapter 6.1, Problem 30E

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Chapter 6 Solutions

EBK WEBASSIGN FOR STEWART'S ESSENTIAL C

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The value of the integral function ∫ 0 t e s sin ( t − s ) d s .

Solution Summary: The author explains the integral function's value and the method of integration by parts.

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To calculate: The value of the integral function ∫0tessin(t−s) ds.

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Chapter 6 Solutions