# Thread: Double ntegral over the first quarter of a circle

1. ## Double ntegral over the first quarter of a circle

Hello from Greece...

Can someone help me solve this exercise please ???

Compute the integral $\int_{0}^{1}\int_{0}^{\sqrt{1-x^2}}(x^2+y^2)dydx$ in the first quarter of a circle with a radius of one

thank you Merry Christmas, Happy Holidays !!!

2. ## Re: HELP with integral in the first quarter of a circle

Originally Posted by kotsos
Hello from Greece...

Can someone help me solve this exercise please ???

Compute the integral $\int_{0}^{1}\int_{0}^{\sqrt{1-x^2}}(x^2+y^2)dydx$ in the first quarter of a circle with a radius of one

thank you Merry Christmas, Happy Holidays !!!

Start by evaluating the inner integral wrt $y$.

3. ## Re: HELP with integral in the first quarter of a circle

Another hint: using polar coordinates you'll obtain $\int_0^{\pi/2}d\theta\int_{0}^1\rho^3\;d\rho$ .

4. ## Re: HELP with integral in the first quarter of a circle

Originally Posted by FernandoRevilla
Another hint: using polar coordinates you'll obtain $\int_0^{\pi/2}d\theta\int_{0}^1\rho^3\;d\rho$ .
i found pi/8=0,3926....is it right ?

5. ## Re: HELP with integral in the first quarter of a circle

Originally Posted by kotsos
i found pi/8=0,3926....is it right ?
Right.

6. ## Re: HELP with integral in the first quarter of a circle

thank you SIR !!!