Posted by Jessica on Tuesday, October 20, 2009 at 9:00pm.
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=1/x^4, y=0, x=2, x=9;
about y=–5

calculus  Reiny, Tuesday, October 20, 2009 at 9:52pm
method: find the volume of the whole solid, then subtract the volume of the cylinder.
Volume of whole solid
= pi(integral)(1/x^4 + 5)^2 dx from 2 to 9
= pi[1/(7x^4)  10/(3x^3 + 25x] from 2 to 9
which came out to 551.077
the volume of the cylinder is
pi(5^2)(7) = 549.779
so the volume of the shape you described is 1.298
not too sure about my arithmetic.
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