# Math Help - Find volume of a solid bound by 2 functions

1. ## Find volume of a solid bound by 2 functions

Fins the volume if the solidobtained by rotating the region bounded by y=x^(1/3) and y=x/4

2. Rotating it about what?. y-axis?. x-axis?. Some other axis?.

Rotated about x-axis using washers:

Find the limits of integration by setting them equal and solving for x. We get x=0 and 8.

${\pi}\int_{0}^{8}(\frac{x^{2}}{16}-x^{\frac{2}{3}})dx$

Using shells rotated about x-axis:

$2{\pi}\int_{0}^{2}y(y^{3}-4y)dy$

3. that was exactly what the book said. I was a bit confused about it too. I think it means rotated about the xaxis

4. Here is a happy little animated diagram showing the region rotated about the x-axis. Enjoy.

And yes, that is what I gave you. Both methods rotating about the x-axis. Shells and washers.

When we use shells, the cross sections are parallel to the axis about which we are revolving. Since they are parallel to the x-axis, we can picture them being stacked up the y-axis. That is why we integate w.r.t y in that case. We solve the equations for x in terms of y and change the limits to the y limits, which are 0 to 2.