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 x-axis. 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)]

## Answer This Question

## Related Questions

- Calculus - The region in the first quadrant bounded by the x-axis, the line x = ...
- AP Calculus - Let R be the first quadrant region enclosed by the graph of y= 2e...
- Calculus - Find the volume of the solid generated by revolving the following ...
- calc - The region in the first quadrant bounded by the x-axis, the line x = &#...
- calculus - Find the volume of the solid generated by revolving the region about ...
- calculus - R is the first quadrant region enclosed by the x-axis, the curve y = ...
- calculus - R is the first quadrant region enclosed by the x-axis, the curve y = ...
- calculus - The region A is bounded by the curve y=x^2-5x+6 and the line y = -x...
- calculus - Which has more area, the region in the first quadrant enclosed by the...
- MATH - Find the volumes of the solids generated by revolving the region in the ...

More Related Questions