How to Find the Volume of a Rotating Solid?

[DrAlexMV]

Homework Statement

Region: f(x) = 2 sin x on the interval [0, π]. Find the volume of
the 3D solid obtained by rotating this region
about the dashed line y = −1.

Homework Equations

Integration of pi∫(2sin(x) + 1)^2 dx

The Attempt at a Solution

http://www3.wolframalpha.com/Calculate/MSP/MSP85361a550f47a75i0g7800002h3g026g9d9ieg7f?MSPStoreType=image/gif&s=3&w=301&h=35

That does not seem to work. I am completely baffled as to what I am doing wrong.

 

[haruspex]

f(x) = 2 sin x on the interval [0, π] does not define a region. It defines a curve and two limits on the x coordinate. You seem to be assuming the remaining boundary is the line y = -1, but why that rather than, say, the x axis?