Question

Find the volume generated by revolving the area bounded by the lines x + y = 5, x = 0

and y = 0, about x-axis.

Answer 1

$V=\pi\int f^2(x)dx=\pi\int_0^5 (5-x)^2dx=\pi(25x-5x^2+x^3/3)|^5_0=125\pi /3$