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a plate occupies an elliptic region G: x^2/4 + y^2/9 less than or equal to 1. the surface density of electric charge is G(x,y)=sin^5(xy^2). Find the total electric charge Q.

Mathematics
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x^2/4 + y^2/4<=1 That's a circle, not an ellipse
o oops it's supposed to be y^2/9

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Other answers:

are you trying to work ou the area of the plate?
so how do i apply G(x,y)=sin^5(xy^2) ?
Apologies, I misread the boundary function as the density function. \[\large \int\limits_{x=-2}^{x=2}\int\limits_{y=0}^{y=\sqrt{9(1-\frac{x^2}{4})}}\sin^5(xy^2)dydx+\int\limits_{x=-2}^{x=2}\int\limits_{y=-\sqrt{9(1-\frac{x^2}{4}}}^{y=0}\sin^5(xy^2)dxdy\] I'm less sure about this one
Swap the last dxdy for dydx
I think that's OK, what do you think about the x-bounds?
i think this is correct. thank you!

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