Posted by Laura on Monday, May 28, 2012 at 11:34pm.
The region in the first quadrant enclosed by the coordinates axes, the line x=pi, and the curve y= cos(cosx) is rotated about the xaxis. What is the volume of the solid generated.

Calculus AB...I really need help  Steve, Tuesday, May 29, 2012 at 4:01am
v = ∫πy^2 dx [0,π]
= ∫πcos^2(cosx) dx [0,π]
that is not something you can evaluate using elementary functions. wolframalpha can do it, but it's done numerically, fer shure!

Calculus AB...I really need help  Count Iblis, Tuesday, May 29, 2012 at 3:40pm
Using cos(2 x) = 2 cos^2(x)  1 and the definition of the Bessel function of zeroth order:
J0(x) = 1/pi Integral from zero to pi of cos[x cos(t)] dt,
you find that the volume is given by:
pi^2/2 [1 + J0(2)]
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