Homework Help: Double integral boundaries.

1. Nov 26, 2011

Kuma

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

D = {x>0, x^2 < y < 10-x^2)

compute

integral (integral D of y^2 sqrt x)

2. Relevant equations

3. The attempt at a solution

I'm having trouble figuring out the bounds of the integral. y goes from x^2 to 10-x^2 but I think I have to split this integral up into two parts. I am not sure how to bound x. The parabolas intersect at the point sqrt 5

2. Nov 26, 2011

flyingpig

What do you mean probably at sqrt(5)? They intersect at two points

3. Nov 26, 2011

Kuma

They intersect at (sqrt 5, 5) and (-sqrt 5, 5). x > 0 so we don't need the negative point.

4. Nov 26, 2011

flyingpig

Yes you got, it

5. Nov 26, 2011

Kuma

So x goes from 0 to sqrt 5? thats the bound for x?

6. Nov 26, 2011

flyingpig

What do you think it should be? Let's put it this way, if it isn't x = 0, where would you start from? You mentioned splitting the integral, how do you plan to do that?

7. Nov 26, 2011

Kuma

I guess I'm overthinking. It looks like x goes from 0 to x^2 and then stops when x reaches sqrt 5, then goes from 10-x^2 back to 0. This is just from the drawing I mean.

8. Nov 27, 2011

Redbelly98

Staff Emeritus
Yes, provided that you integrate over y first -- which, as you said, goes from x^2 to 10-x^2.