# Double Integral

1. Feb 7, 2005

### hytuoc

Plz help me integrating the integral below...I did it to a certain point and got stuck...here is the integral and what I did:
1)
Integral form 0 to pi/2, integral from 0 to a*sin(2*theta), [ r ]dr dtheta
Inner integral: Int from 0 to a*sin(2theta) [(r^2)/2] dr = [a^2 * (sin(2 theta))^2 ] / 2
Outer integral: Int from 0 to pi/2 [a^2 * (sin(2 theta))^2 ] / 2] dtheta
....this is when I dont know how to integrate...plz show me!

2)
Integral from 0 to pi/2, integral from 0 to 1 [sin(r^2)]dr dtheta...how do I integrate this? (how do I integrate sin(r^2)?)
Thanks

2. Feb 7, 2005

### dextercioby

In the 2) exercise,u're missing "r" from the surface element in polar plane coordinates.That "r" should ease your calculations.

As for the first,write it like that.Denote it by J:
$$J=a\int_{0}^{\frac{\pi}{2}} \sin 2\theta \ d\theta \int_{0}^{a} r \ dr$$

And now integrate.

Daniel.

Last edited: Feb 7, 2005