Find the volume of the solid obtained by rotating the region bounded by the curves y = y 0 about the y-axis. Give an exact answer in terms of . = 3x T ²2 and

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Find the volume of the solid obtained by rotating the region bounded by the curves y = 3x - x² and
y = 0 about the y-axis. Give an exact answer in terms of TT.
Transcribed Image Text:Find the volume of the solid obtained by rotating the region bounded by the curves y = 3x - x² and y = 0 about the y-axis. Give an exact answer in terms of TT.
Expert Solution
Step 1: Finding intersection points

To find the volume of the solid obtained by rotating the region bounded by the curves y=3xx2 and y=0 about the y-axis, will use the method of cylindrical shells.

The volume V is given by the formula:

V=2πabxf(x)dx

Where a and b are the x-values where the curves intersect.

First, let's find the intersection points:

3xx2=0

x(3x)=0

This gives us x=0 and x=3 as the intersection points.


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