Question

double integral of e^y/x dy dx with outer limits as 0 and 2 and inner limits as 0 and x^2 ???

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

i may be totally wrong (probably am) but isn't

\[\int_0^{x^2}\frac{e^y}{x}dy=\frac{e^{x^2}-1}{x}\]

Answer 10

@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??

Answer 11

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

Answer 12

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

Answer 13

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...

Answer 14

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

Answer 15

Use parentheses.

e^(y/x) or (e^y)/x?

Answer 16

@chakshu no one can help you until you answer this last question I just asked you lol.

Answer 17

I answered his question through facebook everyone, my connect here sucks
it was e^(y/x)