I am trying to solve the following question. I would be extremely happy if you can provide me with some steps in solving this question. Many Thanks.

Sketch the region bounded by the curves y=2square root of x, x+y=8 and y=1 then find the volume of the solid generated by revolving this region about the x-axis.

Question

I am trying to solve the following question. I would be extremely happy if you can provide me with some steps in solving this question. Many Thanks.

Sketch the region bounded by the curves y=2square root of x, x+y=8 and y=1 then find the volume of the solid generated by revolving this region about the x-axis.

anonymous · Answer

Well, here's a rough sketch of the region.|dw:1422114043713:dw|
Then you just need to do $$\int_0^8 \pi y^2 \, dx$$. You'll want to split into three integrals, though.