Question

using the method of shells, set up, but don't evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1

Answer 1

for shells, we need to integrate on y, since the area is rotated about a horizontal line, and the shells have thickness dy

v = ∫[1,2] 2πrh dy
where r = y-1 and h = x = ln y
v = 2π∫[1,2] (y-1)lny dy

Just use integration by parts to evaluate it.