# Homework Help: Use a double integral to find the volume of the indicated solid

1. Apr 29, 2014

### iRaid

1. The problem statement, all variables and given/known data
Use a double integral to find the volume of the indicated solid.

2. Relevant equations

3. The attempt at a solution
I cant find what I did wrong, it seems like a simple problem...
$$\int_0^2 \int_0^x (4-y^{2})dydx=\int_0^2 4x-\frac{x^{3}}{3}dx$$
$$=2x^2-\frac{x^{4}}{12}|_0^2=8-\frac{16}{12}=\frac{20}{3}$$

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2. Apr 29, 2014

### Zondrina

One of your limits for $y$ is wrong.

3. Apr 29, 2014

### iRaid

I'm not seeing it, sorry.

4. Apr 29, 2014

### Zondrina

If you graph the region in the x-y plane, it should look something like this:

http://gyazo.com/aedf21fdd2006d58eabea7d5b3324065

Suppose you hold $x$ fixed and allow $y$ to vary. Then clearly from the above graph $0 ≤ x ≤ 2$ and $x ≤ y ≤ 2$.

Try letting $y$ be fixed and allowing $x$ to vary now. Do you get the same result?

5. Apr 29, 2014

### iRaid

Ah right, I feel dumb now.

Thank you.