# Thread: Calculating the Volume of a Rotation.

1. ## Calculating the Volume of a Rotation.

Could anyone help me out with these problems? I am having trouble solving them.

Find the volume of the solid obtained by the rotation of y=3x^2-x+4 and y=-x^2+3X+12 about the x-axis.

Find the volume of the solid obtained by rotating the region bounded by x=2y-y^2 and x=y^2-4y about the line y=-3.

2. Originally Posted by ImperialHot
Could anyone help me out with these problems? I am having trouble solving them.

Find the volume of the solid obtained by the rotation of y=3x^2-x+4 and y=-x^2+3X+12 about the x-axis.

Find the volume of the solid obtained by rotating the region bounded by x=2y-y^2 and x=y^2-4y about the line y=-3.
find the x-values of intersection of the two parabolas, $\displaystyle x = a$ and $\displaystyle x = b$ , then use the method of washers ...

$\displaystyle V = \pi \int_a^b [R(x)]^2 - [r(x)]^2 ~dx$

where $\displaystyle R(x)$ is the outer washer radius and $\displaystyle r(x)$ is the inner washer radius.