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# Introduction to the Theorem of Pappus: The region R under the graph of y = x3 from x = 0

ISBN: 9781559536547 285

## Solution for problem 14 Chapter 11-4

Calculus: Concepts and Applications | 2nd Edition

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Problem 14

Introduction to the Theorem of Pappus: The region R under the graph of y = x3 from x = 0 to x = 2 is rotated about the y-axis to form a solid (Figure 11-4p). Figure 11-4p a. Find the area of R. b. Find the volume of the solid using vertical slices of R. c. Find the first moment of area of R with respect to the y-axis. What do you notice about the integral? d. Find the x-coordinate of the centroid of R. e. A theorem of Pappus states that the volume of a solid of revolution equals the area of the region being rotated times the distance the centroid of the region travels. Show that this problem confirms the theorem

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##### ISBN: 9781559536547

The full step-by-step solution to problem: 14 from chapter: 11-4 was answered by , our top Calculus solution expert on 01/25/18, 04:36PM. The answer to “Introduction to the Theorem of Pappus: The region R under the graph of y = x3 from x = 0 to x = 2 is rotated about the y-axis to form a solid (Figure 11-4p). Figure 11-4p a. Find the area of R. b. Find the volume of the solid using vertical slices of R. c. Find the first moment of area of R with respect to the y-axis. What do you notice about the integral? d. Find the x-coordinate of the centroid of R. e. A theorem of Pappus states that the volume of a solid of revolution equals the area of the region being rotated times the distance the centroid of the region travels. Show that this problem confirms the theorem” is broken down into a number of easy to follow steps, and 123 words. This textbook survival guide was created for the textbook: Calculus: Concepts and Applications, edition: 2. Calculus: Concepts and Applications was written by and is associated to the ISBN: 9781559536547. This full solution covers the following key subjects: . This expansive textbook survival guide covers 99 chapters, and 2869 solutions. Since the solution to 14 from 11-4 chapter was answered, more than 214 students have viewed the full step-by-step answer.

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