## anonymous one year ago Which integral correctly computes the volume formed when the region bounded by the curves x2 + y2 = 25, x = 3 and y = 0 is rotated around the y-axis? HELP PLEASE

1. jtvatsim

Have you sketched it out for yourself? I'm beginning to sketch it for myself right now.

2. anonymous

yes I have

3. jtvatsim

From what I'm getting the bounded area is sort of like a pie slice, and the volume looks like a doughnut or something. It's got a big hole through the center.

4. jtvatsim

|dw:1438138779545:dw|

5. anonymous

i know the intefral has sqrt 25-y^2 in it

6. jtvatsim

Yes, that's a good start. We need to take into account the hole as well in order to get the correct integral.

7. jtvatsim

Our slices are basically "washers" or cylinders with holes. From above, the slices look like this:

8. jtvatsim

|dw:1438138974699:dw|

9. jtvatsim

The area of interest is given by taking the big circle area minus the small circle area: $\pi(\sqrt{25-y^2})^2 - \pi(3)^2$ This gives us $\pi(14 - y^2)$ when simplified.

10. anonymous

thank you so much!

11. jtvatsim

Now for the fun part. Integrating that expression! :)

12. jtvatsim

We need to integrate from y = 0 to y = 4... do you want to know how I got the y = 4 or did you figure that out?

13. anonymous

i just needed to know what the integral would be :p

14. anonymous

yes I did

15. jtvatsim

Doing the integration for these problems is sort of the "easy" part right? Imagining and drawing them takes patience and practice. :)

16. jtvatsim

Let me know if you get stuck anywhere on the problem. Good luck!

17. anonymous

drawing it is where I have the most difficulty but you were much help

18. jtvatsim

Yep, just keep practicing and trying to draw things. Look up problems with answers online and just practice the drawing part. Don't even integrate. That might be the best way to master these types of problems. :)