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\[\int\limits_{}^{}\int\limits_{D}^{}y ^{2}e ^{xy}dA\]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.
 one year ago
 one year 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.
 one year ago
 one year ago

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WislarBest ResponseYou've already chosen the best response.0
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.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
dw:1352586388142:dw
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
\[x\le y\le4,~~0\le x\le4\implies0\le x\le y,~~0\le y\le4\]
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
does that make any sense to you?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
so if you switch the order, those would be your bounds where are you stuck?
 one year ago

WislarBest ResponseYou've already chosen the best response.0
How would I break up the integral into iterated sections since the x is in e^(xy)?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
\[\int_0^4\int_0^yy^2e^{yx}dxdy=\int_0^4y\left[\int_0^y ye^{yx}dx\right]dy\]
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
notice that\[\frac{\partial}{\partial x}e^{yx}=ye^{yx}\]
 one year ago

WislarBest ResponseYou've already chosen the best response.0
Alright, so I would have.. \[\int\limits_{0}^{4}ydy*[e ^{xy}0 \ \to\ y]?\]
 one year ago
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