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cse63146

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## Homework Statement

Evaluate the following double integral. Change order of integration if necessary.

[tex]\int^{1}_{0} \int^{x}_{0} x^2 sin(\Pi x y) dy dx[/tex]

## Homework Equations

## The Attempt at a Solution

[tex]\int^{1}_{0} \int^{x}_{0} x^2 sin(\Pi x y) dy dx = -\frac{1}{\Pi}\int^{1}_{0} x cos(\Pi x^2 ) dx[/tex]

Let u = x^2 and du = 2x dx

[tex] - \frac{1}{2 \Pi} \int^{1}_{0} cos (\Pi u) du = -\frac{1}{2 \Pi} \frac{sin (\Pi x^2 )}{\Pi} |^{1}_{0} = - \frac{sin( \Pi)}{2 \Pi^2} = 0[/tex]

but that's wrong. Anyone catch my mistake?

I was also wondering when I'm supposed to change the order of integration. Thanks.

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