Find the volume of the solid obtained by rotating the region enclosed by
y = (x^2) − 1, y = 2x − 1 about y = 4 .
find the imits of integration ...
$\displaystyle x^2-1 = 2x-1$
$\displaystyle x^2 - 2x = 0$
$\displaystyle x(x-2) = 0$
$\displaystyle x = 0$ ... $\displaystyle x = 2$
using the method of washers ...
$\displaystyle R(x) = 4 - (x^2-1)$
$\displaystyle r(x) = 4 - (2x-1)$
$\displaystyle V = \pi \int_0^2 [R(x)]^2 - [r(x)]^2 \, dx$