Explanation Given: The curve y = ( x − 2 ) e x and the x - axis from x = 2 to x = 4 . Approach: The area between curve y = f ( x ) and the x - axis from x = a to x = b : A = ∫ a b f ( x ) d x The integration of by parts ∫ u d v = u v − ∫ v d u Here u ( x ) and v ( x ) differential function. Calculation: Consider the given curve, y = ( x − 2 ) e x . Integrate the given curve from x = 2 to x = 4 that yield area: A = ∫ 2 4 ( x − 2 ) e x d x Perform the integration ∫ ( x − 2 ) e x d x . Let u = x − 2 and d v = e x d x , then: d u = d x Found the v by integrating the function d v = e x d x : ∫ d v = ∫ e x d x After integration: v = e x Substitute e x for v , e x d x for d v , d x for d u and x − 2 for u in the ∫ u d v = u v − ∫ v d u :

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Question

Chapter 8.2, Problem 17E

To determine

To find:

The area between curve y=(x−2)ex and the x- axis from x=2 to x=4.

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Chapter 8.2, Problem 16E

Chapter 8.2, Problem 18E

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