let R be the region between the curves defined by the functions y = x2 and y = 6−x on the interval [−3, 2]. A graph of these two functions and the x- and y-axes is shown above. Use definite integrals and cross-sectional area to find volumes
let R be the region between the curves defined by the functions y = x2 and y = 6−x on the interval [−3, 2]. A graph of these two functions and the x- and y-axes is shown above. Use definite integrals and cross-sectional area to find volumes
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
let R be the region between the curves defined by the functions y = x2
and y = 6−x on the interval [−3, 2]. A graph of these two functions and the x- and y-axes is shown
above.
Use definite integrals and cross-sectional area to find volumes
Set up, but do not evaluate, a definite integral for the volume of the solid obtained
by rotating R about the x-axis.
Draw a typical approximating rectangle of R and the result of revolving this
approximating rectangle about the axis of rotation. Find the volume of this cross-sectional slice.
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