Double ntegral over the first quarter of a circle

Hello from Greece...

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

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

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

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 $\displaystyle \int_{0}^{1}\int_{0}^{\sqrt{1-x^2}}(x^2+y^2)dydx$ 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 $\displaystyle y$.

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

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

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

Quote:

Originally Posted by

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

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

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.

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