## Wislar Group Title $\int\limits_{}^{}\int\limits_{D}^{}y ^{2}e ^{xy}dA$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

1. Wislar

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

|dw:1352586388142:dw|

3. TuringTest

$x\le y\le4,~~0\le x\le4\implies0\le x\le y,~~0\le y\le4$

4. TuringTest

does that make any sense to you?

5. Wislar

Yep, I get that.

6. TuringTest

so if you switch the order, those would be your bounds where are you stuck?

7. Wislar

How would I break up the integral into iterated sections since the x is in e^(xy)?

8. TuringTest

$\int_0^4\int_0^yy^2e^{yx}dxdy=\int_0^4y\left[\int_0^y ye^{yx}dx\right]dy$

9. TuringTest

notice that$\frac{\partial}{\partial x}e^{yx}=ye^{yx}$

10. Wislar

Alright, so I would have.. $\int\limits_{0}^{4}ydy*[e ^{xy}|0 \ \to\ y]?$

11. TuringTest

yes

12. Wislar

Thank you!

13. TuringTest

welcome :D