Explanation Given information: The following curve is given: y 1 = ( 5 − x ) ln x and x − a x i s . Concept use: Integration by parts: ∫ u ( x ) ⋅ v ( x ) ⋅ d x = u ( x ) ∫ v ( x ) ⋅ d x − ∫ [ ( d d x u ( x ) ) ∫ v ( x ) d x ] d x Calculation: To find point of intersection between y 1 = ( 5 − x ) ln x and x − a x i s . Since at x − a x i s , y = 0 Therefore, ( 5 − x ) ln x = 0 5 − x = 0 or ln x = 0 x = 5 or x = 1 So, the point of intersection of the two curves is x = 1 , 5 Therefore, The area enclosed by curves is, A = ∫ 1 5 ( 5 − x ) ln x d x Thus, A = ( ln x ) ∫ 1 5 ( 5 − x ) ⋅ d x − ∫ 1 5 [ ( d d x ( ln x ) ) ∫ 0 5 ( 5 − x ) d x ] d x A = [ ( ln x ) ( 5 x − x 2 2 ) ] 1 5 − ∫ 1 5 1 x ⋅ ( 5 x − x 2 2 ) d x A = [ ( ln x ) ( 5

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

4th Edition

ISBN: 9781319411657

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 7.1, Problem 85E

To determine

To calculate:

The Area between y1=(5−x)lnx and above x−axis.

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Chapter 7.1, Problem 84E

Chapter 7.1, Problem 86E

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Chapter 7 Solutions

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

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