Explanation Given Information: The provided function is ∫ ln ( π / 2 ) ln ( π ) e x sin ( e x ) 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 . If f be a function that is continuous and defined over the interval [ a , b ] , then the integral of the function defined on that interval is given by: ∫ a b f ( u ) d u = F ( b ) − F ( a ) 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 ∫ ln ( π / 2 ) ln ( π ) e x sin ( e x ) d x . Replace the parenthetical expression with variable u . u = e x Determine the derivative of u with respect to x , d u d x = d d x e x d u d x = e x Determine the value of d x , d x = 1 e x d u Replace the value of upper limit b by substituting x = ln ( π ) in e x , b = e x b = e ln ( π ) b = π Replace the value of lower limit a by substituting x = ln ( π 2 ) in e x a = e x a = e ln ( π 2 ) a = π 2 Substitute the value of d x into the integral

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

7th Edition

ISBN: 9781337291293

Author: Waner, Stefan; Costenoble, Steven

Publisher: Brooks Cole

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Chapter 9, Problem 21RE

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To calculate: The integral of the function ∫ln(π/2)ln(π)exsin(ex) dx.

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Chapter 9, Problem 20RE

Chapter 9, Problem 22RE

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Chapter 9 Solutions

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

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The integral of the function ∫ ln ( π / 2 ) ln ( π ) e x sin ( e x ) d x .

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To calculate: The integral of the function ∫ln(π/2)ln(π)exsin(ex) dx.

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Chapter 9 Solutions