Find the Volume: y=x^3 2<=x<=4 around the line y=-1

[pamw]

Find the volume
y=x^3 2<=x<=4 around the line y=-1

I used r=y+1 and h=4-y^(1/3), but I wasn't sure what my bounds should be. I plugged 2 and 4 into x^3 and used 8 and 64 as my bounds, but I got a huge answewr of 15976pi/7, which seems extreme to me.

Am I right? Or did I do something wrong?

 

[galactus]

Your answer isn't that extreme. Actually, not quite extreme enough.

\(\displaystyle \L\\{\pi}\int_{2}^{4}(x^{3}+1)^{2}dx\)