## sanchez9457 Group Title Double Integral: one year ago one year ago

1. sanchez9457 Group Title

$\int\limits_{0}^{1}\int\limits_{0}^{1} xye^xe^y dydx$

2. sanchez9457 Group Title

i just can't quite figure this one out! Anyone willing to help?

3. kirbykirby Group Title

$\int\limits_{0}^{1}\int\limits_{0}^{1}xye^xe^ydydx=\int\limits_{0}^{1}ye^ydy \int\limits_{0}^{1}xe^xdx$ Because the "ye^y dy" part doesn't depend on x, it's like a constant so you can tak it out of the integral. Now you have a multiplication of two integrals that can be done by Integration By Parts... your typical xe^x integral :)

4. kirbykirby Group Title

The answer will be 1 btw

5. tkhunny Group Title

$$\int y\cdot e^{y}\;dy = \int y\;d\left(e^{y}\right) = y\cdot e^{y} - \int e^{y}\;dy$$

6. kirbykirby Group Title

Do you need more help

7. sanchez9457 Group Title

@kirbykirby i really like that answer as you just answered another of my questions!! But i need some clarification if possible:

8. sanchez9457 Group Title

Okay so basically you just said that the double integral equals the multiple of the integral of each variable?

9. kirbykirby Group Title

Yes, In this case you can do it because the term $ye^ydy$in the integral doesn't depend on x (recall you can just switch the dydx to dxdy and not worry about the bounds of integration since they are constants and the same for both integrals). So since ye^y dy doesn't depend on x, it acts like a constant (with respect to x), so you can just move it out of the integral

10. sanchez9457 Group Title

AH!!!!!!!!!!

11. sanchez9457 Group Title

You @kirbykirby are a genius my good sir!

12. kirbykirby Group Title

:) no problem!