A community for students.
Here's the question you clicked on:
 0 viewing
sanchez9457
 3 years ago
Double Integral:
sanchez9457
 3 years ago
Double Integral:

This Question is Closed

sanchez9457
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1}\int\limits_{0}^{1} xye^xe^y dydx\]

sanchez9457
 3 years ago
Best ResponseYou've already chosen the best response.0i just can't quite figure this one out! Anyone willing to help?

kirbykirby
 3 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{0}^{1}\int\limits_{0}^{1}xye^xe^ydydx=\int\limits_{0}^{1}ye^ydy \int\limits_{0}^{1}xe^xdx\] 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 :)

kirbykirby
 3 years ago
Best ResponseYou've already chosen the best response.1The answer will be 1 btw

tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.0\(\int y\cdot e^{y}\;dy = \int y\;d\left(e^{y}\right) = y\cdot e^{y}  \int e^{y}\;dy\)

kirbykirby
 3 years ago
Best ResponseYou've already chosen the best response.1Do you need more help

sanchez9457
 3 years ago
Best ResponseYou've already chosen the best response.0@kirbykirby i really like that answer as you just answered another of my questions!! But i need some clarification if possible:

sanchez9457
 3 years ago
Best ResponseYou've already chosen the best response.0Okay so basically you just said that the double integral equals the multiple of the integral of each variable?

kirbykirby
 3 years ago
Best ResponseYou've already chosen the best response.1Yes, 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

sanchez9457
 3 years ago
Best ResponseYou've already chosen the best response.0You @kirbykirby are a genius my good sir!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.