y = e^x, y = 0, 0 <= x <= 1.
Тогда
V = pi * int (0 1) (e^x)^2 dx = pi * int (0 1) e^(2x) dx =
= pi * (1/2 * e^(2x))_{0}^{1} = pi * (1/2 * e^2 - 1/2 * e^0) =
= pi * (1/2 * e^2 - 1/2) = pi/2 * (e^2 - 1)
Ответ: V = pi/2 * (e^2 - 1).