Explanation Given Information: The integral function is ∫ e − x sin x d x . Formula used: If u and v are two continuous functions of x then D ( u ) is the derivative of u and I ( v ) is the antiderivative of v . Calculation: Consider the provided integral, ∫ e − x sin x d x , To evaluate the integral ∫ e − x sin x d x , suppose that the function u is sin x and v is e − x . Now, evaluate D ( u ) , I ( v ) and record in the table. The steps to create the table are shown below: In the table, in the column D, substitute the value of function u , and in the column I, substitute the value of v . The arrow shows the product of two terms sin x and I ( e − x ) = − e − x . Insert the value of D ( sin x ) = cos x , and in the column I, insert the value of I ( − e − x ) = e − x , The arrow shows the product of two terms as cos x e − x . The minus sign on the left of the table is indicating that the product will appear with a negative sign in the formula. Insert the value of D ( cos x ) = − sin x in column D , the arrow shows the product of D ( cos x ) = − sin x with I ( − e − x ) = e − x . The plus sign on the left of the table is used to indicate that the product will appear with positive sign in the formula

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9.3, Problem 49E

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To calculate: The value of the integral ∫e−xsinx dx using integration by parts.

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Chapter 9.3, Problem 48E

Chapter 9.3, Problem 50E

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Chapter 9 Solutions

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The value of the integral ∫ e − x sin x d x using integration by parts.

Solution Summary: The author calculates the integral's value using integration by parts.

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To calculate: The value of the integral ∫e−xsinx dx using integration by parts.

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Chapter 9 Solutions