# Really hard volume of rotation problem

1. Jan 16, 2013

### iRaid

1. The problem statement, all variables and given/known data

2. Relevant equations
Shell method

3. The attempt at a solution
Not sure if this is right, but the integral I set up is:
$$2\pi \int_0^1 (4-y)(\sqrt{siny})dy$$

Finding the radius is my big problem with these problems, I cant visualize it very well.

Any help is appreciated.

2. Jan 16, 2013

### SammyS

Staff Emeritus
That looks fine except for the limits of integration.

How did you get those limits?

3. Jan 16, 2013

### iRaid

graphing $$\sqrt{siny}$$ from 0 to pi gives me a curve that goes to 1 and back to 0. Since I'm integrating wrt y, I figured it's 0 to 1?

Last edited: Jan 17, 2013
4. Jan 17, 2013

### SammyS

Staff Emeritus
You don't have $\ \ y=\sqrt{\sin(x)}\ \$ with x going from 0 to π.

You have $\ \ x=\sqrt{\sin(y)}\ \$ with y going from 0 to π --- and your integration is w.r.t. y.

5. Jan 17, 2013

### iRaid

Thanks, probably shouldn't agree with wolfram straight after I graph...