## zhiyuan3yu5 2 years ago 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.

1. zhiyuan3yu5

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2. henpen

x^2/4 + y^2/4<=1 That's a circle, not an ellipse

3. zhiyuan3yu5

o oops it's supposed to be y^2/9

4. Rezz5

are you trying to work ou the area of the plate?

5. zhiyuan3yu5

so how do i apply G(x,y)=sin^5(xy^2) ?

6. henpen

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

7. henpen

Swap the last dxdy for dydx

8. henpen

I think that's OK, what do you think about the x-bounds?

9. zhiyuan3yu5

i think this is correct. thank you!