anonymous
  • anonymous
double integral of e^y/x dy dx with outer limits as 0 and 2 and inner limits as 0 and x^2 ???
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
@TuringTest why do we dont change order in this one...ans, is 1/2
anonymous
  • anonymous
\[\int\limits_{0}^{1}\int\limits_{0}^{x^2} e^ y/x dy dx\]
anonymous
  • anonymous
@ kainui then why we change order here let me tag you in one...

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TuringTest
  • TuringTest
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?
anonymous
  • anonymous
m asking that why this question is not solved by changing order of integeration its just solved simply to give ans. as 1/2
hartnn
  • hartnn
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
anonymous
  • anonymous
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
abb0t
  • abb0t
It might help to sketch a picture of the graph first to better explain this.
anonymous
  • anonymous
i may be totally wrong (probably am) but isn't \[\int_0^{x^2}\frac{e^y}{x}dy=\frac{e^{x^2}-1}{x}\]
anonymous
  • anonymous
@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??
anonymous
  • anonymous
then second job would be to compute \[\int_0^1\frac{e^{x^2}-1}{x}dx\]
anonymous
  • anonymous
ohhhhhhhh my bad frnds its e^y/x sorrrrrrrrryyyyyy for that mistake
hartnn
  • hartnn
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...
abb0t
  • abb0t
In general: \[\int\limits \int\limits f(x,y)dA = \int\limits_{a}^{b} \int\limits_{g_1(x)}^{g_2(x)}f(x,y)dydx \]
Kainui
  • Kainui
Use parentheses. e^(y/x) or (e^y)/x?
Kainui
  • Kainui
@chakshu no one can help you until you answer this last question I just asked you lol.
TuringTest
  • TuringTest
I answered his question through facebook everyone, my connect here sucks it was e^(y/x)

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