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## Homework Equations

## The Attempt at a Solution

that is [tex]\int_0^{\sqrt{\pi}}\int_x^{\sqrt{\pi}} \sin(y^2) ~dy ~dx[/tex]

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

[tex]0\leq x\leq y\leq \sqrt{\pi} \Rightarrow [/tex] y ranges from 0 to [tex]\sqrt{\pi}[/tex]

[tex]0\leq x\leq y\leq \sqrt{\pi} \Rightarrow [/tex] x varies from 0 to y.

So the integral is now :

[tex]\int_0^{\sqrt{\pi}}\left(\int_0^y \sin(y^2) ~dx\right)~dy[/tex]

[tex]=\int_0^{\sqrt{\pi}}\left(\sin(y^2)\int_0^y dx\right)~dy[/tex]

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