Chapter 2, Problem 450RE

For the following exercises, find

a.the area of the region,

b.the volume of the solid when rotated around the x-axis, and

c.the volume of the solid when rotated around the y-axis. Use whichever method seems most appropriate to you.

450. Find the center of mass for $\rho ={\tan }^{2}x$ on $x\in (-\frac{\pi }{4},\frac{\pi }{4})$ .