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EXAMPLE 2 Find the volume of the solid obtained by rotating about the x-axis the region under the curve y = Vx from 0 to Illustrate the definition of volume by sketching a typical approximating cylinder.

EXAMPLE 2 Find the volume of the solid obtained by rotating about the x-axis the region under the curve y = Vx from 0 to Illustrate the definition of volume by sketching a typical approximating cylinder.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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EXAMPLE 2 Find the volume of the solid obtained by rotating about the x-axis the region under the curve y = vx from 0 to 7. Illustrate the definition of volume by sketching a typical approximating cylinder. SOLUTION The region is shown in the top figure with b = 7. If we rotate about the x-axis, we get the solid shown in the bottom figure. When vwe slice through the point x, we get a disk with radius Vx. The area of the cross-section is A(x) = and the volume of the approximating cylinder (a disk with thickness Ax) is A(x)Ax = Ax. The solid lies between x = 0 and x = 7, so its volume is V = A(x) dx dx A.r
Transcribed Image Text:EXAMPLE 2 Find the volume of the solid obtained by rotating about the x-axis the region under the curve y = vx from 0 to 7. Illustrate the definition of volume by sketching a typical approximating cylinder. SOLUTION The region is shown in the top figure with b = 7. If we rotate about the x-axis, we get the solid shown in the bottom figure. When vwe slice through the point x, we get a disk with radius Vx. The area of the cross-section is A(x) = and the volume of the approximating cylinder (a disk with thickness Ax) is A(x)Ax = Ax. The solid lies between x = 0 and x = 7, so its volume is V = A(x) dx dx A.r
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