Originally Posted by

**Kimberly** Just needed to check something with you math experts ;o)

1. Find the volume of the solid obtained by rotating the region bounded by $\displaystyle y=\sqrt[6]{x}$ and $\displaystyle y=x$, rotated about the line $\displaystyle y=1$

Is it

$\displaystyle \int_0^1\pi{(1-\sqrt[6]{x})-(1-x)}$ ??

2. Same premise as the previous problem, but with the following data:

region bounded by $\displaystyle y=x^4$ and $\displaystyle x=y^4$, rotated about $\displaystyle x=-1$

Now, this really got me. Am I supposed to put it all in terms of $\displaystyle x$, so that the regions would be $\displaystyle y=x^4$ and $\displaystyle y=\sqrt[4]{x}$ ?? I'm having a little trouble graphing these... but I think the lower limit is zero...?

Lastly,

3. When I'm told to use the method of cylindrical shells to find a volume, is that the following equation:

$\displaystyle \int_a^b{2\pi}({r})({h})dx$ ??

Thank you for your help!