## rainbow22 Group Title find the volume of the solid formed by revolving the region bounded by y=x^2, y=0, and x=2 about the y axis one year ago one year ago

1. Thomas9 Group Title

Do you know about multivariable calculus perhaps? Or do you want the easy-not-understanding-what-you're-doing way

2. rainbow22 Group Title

3. rainbow22 Group Title

No, I am supposed to use the Disk Washer method. I can do it with antiderive(2-y) to get the right answer but I'm pretty sure that's not following th formula I'm given which is outer radius minus inner radius.

4. Thomas9 Group Title

Disk Washer?

5. rainbow22 Group Title

There's a hole in the solid.. so it's called Washer Method.

6. Thomas9 Group Title

So how does this method work?

7. rainbow22 Group Title

I do antiderivative from a-b in terms of x or y (y in this case because I rotate about y axis) pi (outer radius)^2 - (inner radius)^2

8. rainbow22 Group Title

$\int\limits_{a}^{b} \pi (outer radius)^2 -(innerradius)^2 dx$

9. Thomas9 Group Title

I don't how that works, I'm afraid.

10. zepdrix Group Title

|dw:1359838432884:dw|

11. zepdrix Group Title

|dw:1359838561883:dw|So let's look at one slice.

12. zepdrix Group Title

Oh you're doing the washer/disk method, my mistake.. Lemme slice that differently.

13. zepdrix Group Title

|dw:1359838731527:dw|Ok this type of slice will give us a Disk.

14. zepdrix Group Title

|dw:1359838764034:dw|So we want to get the Volume of this disk.

15. zepdrix Group Title

The outer radius appears to be the line x=2. And the inner radius our function which is in terms of x, we'll need it in terms of y to integrate since we sliced in the y direction (dy thickness)

16. zepdrix Group Title

$\large y=x^2 \qquad \rightarrow \qquad x=\sqrt y$

17. zepdrix Group Title

$\large V=\pi\left[(2)^2-(\sqrt y)^2\right]dy$

18. zepdrix Group Title

Then to find the total volume in this enclosed area, we Integrate (add up all the slices) from one intersecting point to another. Where do they intersect? Ummm looks like.. y=0 and y=4?

19. zepdrix Group Title

Simplifying things down gives us, $\large \pi \int\limits_0^4 4-y \;dy$

20. zepdrix Group Title

Imma check my work real quick to make sure I didn't make a mistake somewhere. A little tired, it's possible. lol

21. zepdrix Group Title

Yah I think that's right. Confused about any of that? I went through it a little sloppy D:

22. rainbow22 Group Title

It's right. I realize what I did wrong! I had the wrong intersections/points. I did instead from -2 to 2.. not realizing that it was based on terms of y . thank you so much!

23. zepdrix Group Title

Oh cool c: