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Wislar

  • 3 years ago

\[\int\limits_{}^{}\int\limits_{D}^{}y ^{2}e ^{xy}dA\]D is bounded by y=x. y=4, x=0 Set up iterated integrals for both orders of integration. Then evaluate the integral using the easier order and explain why it is easier.

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  1. Wislar
    • 3 years ago
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    I know I can do... \[\int\limits_{0}^{4}\int\limits_{x}^{4}y ^{2}e ^{xy}dydx\]but I'm not sure what they mean by both orders of integration and how to find the other orders.

  2. TuringTest
    • 3 years ago
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    |dw:1352586388142:dw|

  3. TuringTest
    • 3 years ago
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    \[x\le y\le4,~~0\le x\le4\implies0\le x\le y,~~0\le y\le4\]

  4. TuringTest
    • 3 years ago
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    does that make any sense to you?

  5. Wislar
    • 3 years ago
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    Yep, I get that.

  6. TuringTest
    • 3 years ago
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    so if you switch the order, those would be your bounds where are you stuck?

  7. Wislar
    • 3 years ago
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    How would I break up the integral into iterated sections since the x is in e^(xy)?

  8. TuringTest
    • 3 years ago
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    \[\int_0^4\int_0^yy^2e^{yx}dxdy=\int_0^4y\left[\int_0^y ye^{yx}dx\right]dy\]

  9. TuringTest
    • 3 years ago
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    notice that\[\frac{\partial}{\partial x}e^{yx}=ye^{yx}\]

  10. Wislar
    • 3 years ago
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    Alright, so I would have.. \[\int\limits_{0}^{4}ydy*[e ^{xy}|0 \ \to\ y]?\]

  11. TuringTest
    • 3 years ago
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    yes

  12. Wislar
    • 3 years ago
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    Thank you!

  13. TuringTest
    • 3 years ago
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    welcome :D

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