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zhiyuan3yu5 Group Title

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.

  • 2 years ago
  • 2 years ago

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  1. zhiyuan3yu5 Group Title
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    |dw:1353266741808:dw|

    • 2 years ago
  2. henpen Group Title
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    x^2/4 + y^2/4<=1 That's a circle, not an ellipse

    • 2 years ago
  3. zhiyuan3yu5 Group Title
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    o oops it's supposed to be y^2/9

    • 2 years ago
  4. Rezz5 Group Title
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    are you trying to work ou the area of the plate?

    • 2 years ago
  5. zhiyuan3yu5 Group Title
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    so how do i apply G(x,y)=sin^5(xy^2) ?

    • 2 years ago
  6. henpen Group Title
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    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

    • 2 years ago
  7. henpen Group Title
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    Swap the last dxdy for dydx

    • 2 years ago
  8. henpen Group Title
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    I think that's OK, what do you think about the x-bounds?

    • 2 years ago
  9. zhiyuan3yu5 Group Title
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    i think this is correct. thank you!

    • 2 years ago
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