Cyndrical Shells Calculus Problem?!?!?

Question

Use the methods of cyndrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

x + y = 3 and x = 4 - (y -1)^2

Answer 1

You'll have to break this one up a little.

From x-values ranging from 0 to 3, you will want to integrate with respect to y from 4 - (y-1)^2 down to 3 - y.

For 3 <= x <= 4, you need to integrate from 4 - (y-1)^2 down to 1...and then *double* that. If you draw the picture, you'll see why.

Finally, you will be ready to rotate around the x-axis.

I'll have to work out the details later, since I can't do that on the job.