# Thread: calculating domain in double integral problem

1. ## calculating domain in double integral problem

Hi,

I have been set the following question;

D f(x,y) dxdy, where f(x,y)=xy^2, and D is the region in the first quadrant bounded by the curves y=x^2, and x=y^2.

The integration part I don't have a problem with, but I need some advice on how I calculate the limits from the domain statement. I assume that the answer is 0 to 1, based on common sense, but would appreciate of someone could explain how I can show the calculation of this.

2. Write the area of the region D as a definite integral with respect to y:

$\int_0^1 \sqrt{y}\ -\ y^2\ dy$

where the integrand is the length of any Reimann strip. Then you can easily convert that to a double integral of 1 with respect to dx dy.

$\int_0^1\ \int_{y^2}^{\sqrt{y}}\ 1\ dx\ dy$