Consider the region r x y isin r2 0 le x le 1 and 0 le y

Question

Consider the region R = {(x, y) ∈ R^2| 0 ≤ x ≤ 1 and 0 ≤ y ≤ e^2x}.

(a) Draw R and calculate the volume of revolution obtained by rotating region R about the y-axis.

(b) Rotate region R about the line y = -1 and find the volume of the resulting solid.