Explanation Given: The volume of the solid generated is given by: y = ( − ln x ) Formula used: To check for convergence, the following limit must exist. ∫ a b f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x According to the by parts formula: I = u v − ∫ v ⋅ u ′ . Calculation: The function given is solved within the limits, 0 < x < 2 , as V = π ∫ 0 1 ( − ln x ) 2 d x = π lim b →

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ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 8.8, Problem 104E

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To calculate: The volume of solid generated by revolving the unbounded region between y=−lnx, y-axis and x-axis.

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Chapter 8.8, Problem 103E

Chapter 8.8, Problem 105E

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The volume of solid generated by revolving the unbounded region between y = − ln x , y -axis and x -axis.

Solution Summary: The author calculates the volume of the solid generated by revolving the unbounded region between y=-mathrmlnx.

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To calculate: The volume of solid generated by revolving the unbounded region between y=−lnx, y-axis and x-axis.

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Chapter 8 Solutions