Explanation Given: The equation is y = 6 − x 2 − ln x ; 1 ≤ x ≤ 4 . Calculation: Use online graphing calculator to graph the given function y = 6 − x 2 − ln x ; 1 ≤ x ≤ 4 . From Figure 1, it is clear that the curve intersects x -axis at the point (2.275,0). Calculate the area between the curve and the x axis over that interval. ∫ 1 2.275 y d x + | ∫ 2.275 4 y d x | (1) First, integrate the given function ∫ ( 6 − x 2 − ln x ) d x . ∫ ( 6 − x 2 − ln x ) d x = ∫ 6 d x − ∫ x 2 d x − ∫ ln x d x ( ∵ u = ln ( x ) , d v = 1 ) = 6 x − x 3 3 − ( x ln ( x ) − ∫ 1 d x ) ( ∵ d u = 1 x , v = x ) = 6 x − x 3 3 − ( x ln ( x ) − x ) + C Apply the upper limit and lower limit of the integral ∫ 1 2.275 ( 6 − x 2 − ln x ) d x . ∫ 1 2.275 ( 6 − x 2 − ln x ) d x = [ 6 x − x 3 3 − ( x ln ( x ) − x ) ] 1 2.275 = ( 6 ( 2.275 ) − ( 2.275 ) 3 3 − ( 2.275 ln ( 2.275 ) − 2.275 ) ) − ( 6 ( 2.275 ) − ( 2

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Chapter 6.3, Problem 60E

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To sketch: The graph and find the area between the curve and the x axis over that interval.

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Chapter 6.3, Problem 59E

Chapter 6.3, Problem 61E

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Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

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