Find the volume generated by rotating the region

Question

Find the volume generated by rotating the region in the first quadrant bounded by y=e^x and the x-axis from x=0 to x=ln(2) about the y-axis.  Express your answer in exact form.

Volume = 

Answer 1

By shell method volume v = 2π∫₀^ln2xe^xdx = 2π(xe^x - e^x)₀^ln2 = 2π(2ln2 - 2 + 1) = 2π(2ln2 - 1)