## chakshu Group Title double integral of e^y/x dy dx with outer limits as 0 and 2 and inner limits as 0 and x^2 ??? one year ago one year ago

1. chakshu Group Title

@TuringTest why do we dont change order in this one...ans, is 1/2

2. chakshu Group Title

$\int\limits_{0}^{1}\int\limits_{0}^{x^2} e^ y/x dy dx$

3. chakshu Group Title

@ kainui then why we change order here let me tag you in one...

4. TuringTest Group Title

I'm sorry, I'm either really tired or confused. It seems to me that this integral can only be done by changing the bounds. Is that what you are saying @chakshu ? You are asking why we have to change the bonds?

5. chakshu Group Title

m asking that why this question is not solved by changing order of integeration its just solved simply to give ans. as 1/2

6. hartnn Group Title

i will repeat turing's word. in last Q, it was difficult to integrate w.r.t y after x was integrated, thats why bounds were changed. in this case, its easy to integrate without changing bounds

7. chakshu Group Title

http://openstudy.com/users/chakshu#/updates/5080305ee4b0b56960054f2d this is another questn that involves changing order i just wanna knoe the theoritical differnce that when do we have to change order to integerate ????hope this is simple to understnd

8. abb0t Group Title

It might help to sketch a picture of the graph first to better explain this.

9. satellite73 Group Title

i may be totally wrong (probably am) but isn't $\int_0^{x^2}\frac{e^y}{x}dy=\frac{e^{x^2}-1}{x}$

10. chakshu Group Title

@hartnn so ur sayin since in previous questn we had difficult limts so we changed order and in this one we have easy limits so we dont??

11. satellite73 Group Title

then second job would be to compute $\int_0^1\frac{e^{x^2}-1}{x}dx$

12. chakshu Group Title

ohhhhhhhh my bad frnds its e^y/x sorrrrrrrrryyyyyy for that mistake

13. hartnn Group Title

its not about limits, its about what u get after integrating w.r.t one of the variables, sometimes the resulting function is very difficult to integrate w.r.t other variable...

14. abb0t Group Title

In general: $\int\limits \int\limits f(x,y)dA = \int\limits_{a}^{b} \int\limits_{g_1(x)}^{g_2(x)}f(x,y)dydx$

15. Kainui Group Title

Use parentheses. e^(y/x) or (e^y)/x?

16. Kainui Group Title