Double ntegral over the first quarter of a circle

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December 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)
December 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 $y$ .
December 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 $\int_0^{\pi/2}d\theta\int_{0}^1\rho^3\;d\rho$ .
December 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 ?
December 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.
December 21st 2011, 04:02 AM
kotsos

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

thank you SIR !!!

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