Explanation Formula used: Maclaurin expansion of e x : “The Maclaurin expansion of e x is given by, e x = 1 + x + x 2 2 ! + x 3 3 ! + x 4 4 ! + ⋯ ” Calculation: Replace x by − x in the Maclaurin expansion of e x and obtain the Maclaurin expansion of e − x as follows. e − x = 1 − x + ( − x ) 2 2 ! + ( − x ) 3 3 ! + ( − x ) 4 4 ! + ⋯ = 1 − x + x 2 2 − x 3 6 + ⋯ Given that, the region is bounded by y = e − x , y = 0 , x = 0 and x = 0.1 . Then the volume of the region revolved about y –axis is V = ∫ 0 0.1 2 π x e − x d x . Now substitute the Maclaurin expansion of e − x and evaluate the integral as shown below. V = 2 π ∫ 0 0

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Chapter 30, Problem 66RE

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The volume generated by the region bounded by y=e−x, y=0, x=0 and x=0.1 revolved about y -axis.

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Chapter 30, Problem 65RE

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Chapter 30 Solutions

Basic Technical Mathematics

Ch. 30.1 - Prob. 1PE Ch. 30.1 - Prob. 2PE Ch. 30.1 - Prob. 1E Ch. 30.1 - Prob. 2E Ch. 30.1 - Prob. 3E Ch. 30.1 - Prob. 4E Ch. 30.1 - Prob. 5E Ch. 30.1 - Prob. 6E Ch. 30.1 - Prob. 7E Ch. 30.1 - Prob. 8E

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The volume generated by the region bounded by y = e − x , y = 0 , x = 0 and x = 0.1 revolved about y -axis.

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