Double ntegral over the first quarter of a circle

**kotsos** · December 20th 2011, 11:30 PM

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 !!!

**alexmahone** · December 20th 2011, 11:34 PM

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 $y$ .

**FernandoRevilla** · December 21st 2011, 12:10 AM

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

**kotsos** · December 21st 2011, 03:27 AM

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 ?

**FernandoRevilla** · December 21st 2011, 03:45 AM

Originally Posted by kotsos

i found pi/8=0,3926....is it right ?

Right.

**kotsos** · December 21st 2011, 04:02 AM

thank you SIR !!!

Thread: Double ntegral over the first quarter of a circle