# Help with yet another solid of revolution question

1. Jan 28, 2014

### student93

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

See the attached problem.

2. Relevant equations

See the attached problem.

3. The attempt at a solution

I used washer method and got an inner radius of x=y^2 and an outer radius of x=y+2, I calculated my upper limit as being 4 and my lower limit as being 0. The answer is 72π/5, but I can't seem to get that answer. Are my limits of integration wrong and/or did I use the wrong method?

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2. Jan 28, 2014

### haruspex

That method works for me. Please post your detailed steps.

3. Jan 28, 2014

### student93

V=π∫(y+2)^2 - (y^2)^2 dy, from 0 to 4
V= -2032π/15, which is obviously not the correct answer since volume can't be negative etc.

4. Jan 28, 2014

### haruspex

Right integrand, wrong range. x goes from 0 to 4. what's the range for y?

5. Jan 28, 2014

### student93

I set √x=x-2, and solved the quadratic and got x=4,1 (I used the 4 as my upper limit and used 0 as my lower limit since it seemed that 0 was the lower limit from how the graph looked). Also how exactly do I go about calculating the limits of integration in regards to y?

6. Jan 28, 2014

### haruspex

Yes, but you are integrating with respect to y, so your bounds must be bounds on y, not x.
Sketch the curves and see where they cross.

7. Jan 28, 2014

### student93

I set the equations equal and I get my upper limit as 4 with respect to y and my lower limit as 1 with respect to y, however I still don't get the correct answer which is 72π/5.

Last edited: Jan 28, 2014
8. Jan 28, 2014

### student93

So I finally realized I was supposed to solve y^2=y+2 and get an upper and lower limit of 2 and -1 respectively. After plugging in those two values into the integrand, I finally ended up getting the correct answer. Thanks for the help.