# Proving Inequality

1. Oct 28, 2013

### PsychonautQQ

1. The problem statement, all variables and given/known data
Prove the inequality double integral (dA / (4+x^2+y^2)) is less than or equal to pi, where the double integral has a sub D where D is the disk x^2 + y^2 less than or equal to four

2. Relevant equations

3. The attempt at a solution
I really have no idea, anyone want to give me a clue to help me get started?

2. Oct 28, 2013

### dirk_mec1

Are you sure this is the exact question?

Last edited: Oct 28, 2013
3. Oct 28, 2013

### Staff: Mentor

I believe it is.

Here's the integral and inequality:
$$\int_D \frac{dA}{4 + x^2 + y^2} \leq \pi$$
where D is the disk x2 + y2 ≤ 4.

The key here, I believe, is that $\frac{1}{4 + x^2 + y^2} \leq \frac 1 4$.

4. Oct 28, 2013

### dirk_mec1

Are you really sure?

5. Oct 28, 2013

### Office_Shredder

Staff Emeritus
Obvously only Psychonaut can be sure but the problem statement is a true statement if that's what you're trying to get at.

6. Oct 28, 2013

### dirk_mec1

What do you mean by a "true statement"?

$$\int_0^4 \frac{r}{4+r^2}\ \mbox{d}r = \ln(\sqrt5) = 0.8$$

7. Oct 28, 2013

### Staff: Mentor

By "true statement" I think Office_Shredder means that the problem as described in the OP represents a problem that can be solved. In this case, the problem is fairly simple. If I'm missing something, please enlighten me.

8. Oct 28, 2013

### D H

Staff Emeritus
You have the wrong integration limits here. They should be from 0 to 2, not from 0 to 4.