# How do I solve this double integral?

• Nov 8th 2009, 08:50 PM
Infernorage
How do I solve this double integral?
Here is the double integral I need to solve...

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

Can someone solve this and tell me how to do it. I tried solving it, but the first integral came out to be something I can't take a second integral of, so unless I am supposed to use Riemann sums or something like that it must be wrong. Thanks in advance.
• Nov 8th 2009, 09:57 PM
Jhevon
Quote:

Originally Posted by Infernorage
Here is the double integral I need to solve...

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

Can someone solve this and tell me how to do it. I tried solving it, but the first integral came out to be something I can't take a second integral of, so unless I am supposed to use Riemann sums or something like that it must be wrong. Thanks in advance.

how did you take the first integral??

you must change the order of integration. the integral becomes, $\int_0^1 \int_0^x e^{y/x}~dy~dx$. And that you should be able to do.
• Nov 8th 2009, 10:29 PM
Infernorage
Quote:

Originally Posted by Jhevon
how did you take the first integral??

you must change the order of integration. the integral becomes, $\int_0^1 \int_0^x e^{y/x}~dy~dx$. And that you should be able to do.

Can you explain to me why the limits changed? Why does the limit for the y integral now go from 0 to x and why is the bottom limit of the x integral 0 instead of x=y? Sorry, just a little confused about that.
• Nov 8th 2009, 10:37 PM
Jhevon
Quote:

Originally Posted by Infernorage
Can you explain to me why the limits changed? Why does the limit for the y integral now go from 0 to x and why is the bottom limit of the x integral 0 instead of x=y? Sorry, just a little confused about that.

The first step is to sketch the region you are integrating over. Then describe the shaded region such that x goes between constants and y goes between functions.

the limits changed because the integral would be "impossible" to do without doing that.