# Evaluate the double integral?

1. Feb 9, 2015

### Math10

1. The problem statement, all variables and given/known data
Evaluate the double integral (x+2y)dA, where R is the region in the first quadrant bounded by the circle x^2+y^2=9.

2. Relevant equations
None.

3. The attempt at a solution
I know how to evaluate the double integral but I just don't know how to find the limits of integration. I know that the radius of the circle is 3.

2. Feb 9, 2015

### PeroK

First, what are the limits for x?

3. Feb 9, 2015

### Math10

I have no idea. Is it 0 to 3?

4. Feb 9, 2015

### PeroK

It looks like you do have an idea. That's right.

For each x, what are the limits of y? You may need to draw the area.

5. Feb 9, 2015

From 0 to 3?

6. Feb 9, 2015

### Staff: Mentor

How would you describe the region R as a set? IOW, R = {(x, y) | <inequality involving x> and <inequality involving y>}.

If you are tempted to write the inequalities as $0 \le x \le 3, \text{and } 0 \le y \le 3$, resist that temptation! That region would be a square, which the one in this problem is not.

As I said in another of your threads, many times carrying out the integration is the easy part, requiring very little thinking. Figuring out the limits of integration is often the more difficult task. Your textbook should have a number of examples. Have you looked at them?

7. Feb 9, 2015

### PeroK

That would be a square in the first quadrant.

8. Feb 9, 2015

### Math10

So y=sqrt(9-x^2) and y= - sqrt(9-x^2)?

9. Feb 9, 2015

### PeroK

Why would y be negative?

10. Feb 9, 2015

### Math10

So y=0 to sqrt(9-x^2)?

11. Feb 9, 2015

### Staff: Mentor

Yes. Now what are your limits for x?

12. Feb 9, 2015

### Math10

0 to 3?

13. Feb 9, 2015

### Staff: Mentor

Yes. Now you need to figure the order in which you're going to integrate.

14. Feb 9, 2015

### Math10

dy dx?

15. Feb 9, 2015

### Staff: Mentor

You tell me ...

16. Feb 9, 2015

### Math10

dy dx.

17. Feb 9, 2015

### Staff: Mentor

OK. Now you're ready to set up the iterated integral and evaluate it...

18. Feb 10, 2015

### Math10

Thank you!

19. Feb 10, 2015

### Staff: Mentor

You're welcome!