Find the volume of the solid obtained by rotating the region enclosed by

y = (x^2) − 1, y = 2x − 1 about y = 4 .

- Dec 4th 2008, 10:46 AMderrickdFind the volume of the solid obtained by rotating the region enclosed by
Find the volume of the solid obtained by rotating the region enclosed by

y = (x^2) − 1, y = 2x − 1 about y = 4 . - Dec 4th 2008, 02:21 PMderrickd
bump

- Dec 4th 2008, 03:30 PMskeeter
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 ...

$\displaystyle R(x) = 4 - (x^2-1)$

$\displaystyle r(x) = 4 - (2x-1)$

$\displaystyle V = \pi \int_0^2 [R(x)]^2 - [r(x)]^2 \, dx$