Volume Calculus

Question

Consider the solid obtained by rotating the region bounded by the given curves about the line y = 4.

Find the volume V of this solid.

Answer 1

V = integral from x = 0 to x = 2 of Area of washer dx

Area of washer = pi(r_o² - r_i²) and r_o = 4 - 2e^-x and r_i = 2 so:

V = pi*(integral from 0 to 2 of [(4 - 2e^-x)² - 2²]dx) = 38.1