(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f(x,y) = sin(∏*y^2). Let R be the triangular region on the x-y plane with the vertices at (0,0) (0,1) (.5,1). Consider the solid that is under z = f(x,y) and over the region R. Calculate the volume over that region using double integrals.

2. Relevant equations

3. The attempt at a solution

∫[itex]^{1}_{0}[/itex]∫[itex]^{1}_{.5}[/itex]sin(∏*y^2) dxdy

Integrating with respect to x first gives

.5∫[itex]^{1}_{0}[/itex]sin(∏*y^2)dy.

After this i'm stuck because I know there is no simple anti-derivative for that function.

If you reverse the order of integration then, sin(∏*y^2) would have to be integrated at first as well, so not sure what to do.

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# Double Integral over a triangular region

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