# Double ntegral over the first quarter of a circle

• Dec 20th 2011, 11:30 PM
kotsos
Double ntegral over the first quarter of a circle
Hello from Greece...

Can someone help me solve this exercise please (Worried) ???

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 (Smirk)

thank you Merry Christmas, Happy Holidays !!!(Happy)

• Dec 20th 2011, 11:34 PM
alexmahone
Re: HELP with integral in the first quarter of a circle
Quote:

Originally Posted by kotsos
Hello from Greece...

Can someone help me solve this exercise please (Worried) ???

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 (Smirk)

thank you Merry Christmas, Happy Holidays !!!(Happy)

Start by evaluating the inner integral wrt $y$.
• Dec 21st 2011, 12:10 AM
FernandoRevilla
Re: HELP with integral in the first quarter of a circle
Another hint: using polar coordinates you'll obtain $\int_0^{\pi/2}d\theta\int_{0}^1\rho^3\;d\rho$ .
• Dec 21st 2011, 03:27 AM
kotsos
Re: HELP with integral in the first quarter of a circle
Quote:

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 ?
• Dec 21st 2011, 03:45 AM
FernandoRevilla
Re: HELP with integral in the first quarter of a circle
Quote:

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

Right.
• Dec 21st 2011, 04:02 AM
kotsos
Re: HELP with integral in the first quarter of a circle
thank you SIR !!!