compute the double integral

from [0,sqrt(pi)]x[x,sqrt(pi)]

how can I compute sin(y^2)

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- May 16th 2009, 11:45 PMyzc717integral
compute the double integral

from [0,sqrt(pi)]x[x,sqrt(pi)]

how can I compute sin(y^2) - May 17th 2009, 01:35 AMCaptainBlack
- May 17th 2009, 01:41 AMMoo
Hello,

One can guess that and

that is

Reverse the order of the integrals (which is possible since the integrand is positive) :

y ranges from 0 to

x varies from 0 to y.

So the integral is now :

And that's easier :p - May 17th 2009, 01:47 AMyzc717
- May 17th 2009, 02:11 AMMoo
The inner integral will give y.

Which finally gives

For this one : substitution !