1. Volume :S blah

I find it really hard trying to imagine what the picture is after rotation! :S Help please!

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

2. Originally Posted by MathNeedy18
I find it really hard trying to imagine what the picture is after rotation! :S Help please!

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

$\displaystyle V= \int_a^b 2\pi x f(x) \, dx$, since it is rotated on the y-axis..
$\displaystyle f(x) = x(8-x) = 8x-x^2$
so, if we substitute these infos, we have $\displaystyle V= \int_0^8 2\pi (8x^2 - x^3) \, dx$