Set up the definite intergrols but don'tEvaluate.a) Volume of a solid obtained by revolvingabout theby y on the left by the linX=114 and below bq y=1yaxis He region boonded aboneb) Volume of a Solid obtained by revolvingabout the k-axis.graph y=sin x cos .the region bulow theover the interval 0.

Answered: a) Volume of a solid obtained by…

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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Set up the definite intergrols but don't
Evaluate.
a) Volume of a solid obtained by revolving
about the
by y on the left by the lin
X=114 and below bq y=1
yaxis He region boonded abone
b) Volume of a Solid obtained by revolving
about the k-axis.
graph y=sin x cos .
the region bulow the
over the interval 0.

Expert Solution

Step 1

Concept introduction:

Shell method

The volume for solid of revolution between curves is the volume of an object between a curve $y = f (x)$ and a curve $y = g (x)$ rotated around the y-axis on the interval $[a, b]$ , where $0 \leq g (x) \leq f (x)$ given by $V = 2 π \int_{a}^{b} x [f (x) - g (x)] d x$ .

Disk method

The volume for solid of revolution between curves is the volume of an object determined by a curve $f (x)$ rotated around the x-axis on the interval $[a, b]$ given by $V = \int_{a}^{b} π {(f (x))}^{2} d x$ .

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