# Thread: Volume using shell method--help?!

1. ## Volume using shell method--help?!

Hey guys, i was wondering if you can help me out with this problem...

Use the shell method to find the volume generated by rotating the region bounded by the given curves about the y-axis.

1. $\displaystyle y=x^2,$ $\displaystyle y=4,$& $\displaystyle x=0$ (Answer is:$\displaystyle 8pi$)
2. $\displaystyle y = ln(x),$ $\displaystyle y=0,$& $\displaystyle x=e$(Answer is: $\displaystyle \frac{\pi(e^2+1)}{2}$)

Thanks!

2. Solid of revolution - Wikipedia, the free encyclopedia

Best to draw a graph of the region to be revolved.

Suppose integrating with respect to x... mark in a little 'Reimann strip'.

Imagine revolving the strip around the y-axis... yes, a cylindrical shell, so you're integrating with respect to the right variable for shells.

And the expression to integrate will be the circumference 2 pi x times the length of the strip. (4 - x^2 the first time and ln(x) - 0 the second.)

If you've drawn the sketch the limits will be apparent.

3. thanks, but for number 1, it says that x=0 and the problem does not mention how far it goes to; or is it automatically 1 when it's not mentioned?

4. oh never mind i got it. i graphed it and got the answers. thanks a lot for you help n__n i greatly appreciate it.