(a) Explanation Given information: The function inside the integrand is ( 1 x ) 2 having its domain starting from 1 and extending till infinity. Formula: ∫ c d x n d x = [ x n + 1 n + 1 ] c d Calculation: Express the integral as below. ∫ 1 ∞ π ( 1 x ) 2 d x Simplify it as below. ∫ 1 ∞ π ( 1 x ) 2 d x = (b) To determine Explain the apparent contradiction in able to cover an infinite surface area while filling the horn with a finite amount of paint.

14th Edition

ISBN: 9780135420683

Author: Hass

Publisher: PEARSON

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Question

Chapter 8.8, Problem 82E

(a)

To determine

The value of an improper integral and prove that the term converges.

(b)

To determine

Explain the apparent contradiction in able to cover an infinite surface area while filling the horn with a finite amount of paint.

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Chapter 8.8, Problem 81E

Chapter 8.8, Problem 83E

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