# Double Integrals

• Feb 28th 2007, 04:36 PM
macabre
Double Integrals
Ok so i'm rather stuck on this one question, help would be much appreciated:

I have used the capital S as an integral sign with the values above and below it as the limits of the integration, also please ignore the underscores, i put them in to aid with the spacing

by changing the order of integration, evaluate

y=4 x=y^0.5
S_____S______exp(y/x) dx dy
y=0 x=(y/2)

Draw a sketch of the area and directions of integration.

• Feb 28th 2007, 04:57 PM
Soroban
Hello, macabre!

Quote:

By changing the order of integration, evaluate:

. . y=4 . .x=y^½
. .
. . . . . e(y/x) dx dy
. .y=0 . . x=½y

Draw a sketch of the area and directions of integration.

Code:

```        |       4+        *         |      *:|         |    *::*|         |  *:::* |         | *:::*  |       - * - - - - + -         |        2```

. . x=2 . y=2x
. .
. . . . . e^{y/x} dy dx
. . x=0 . y=x²

• Feb 28th 2007, 05:24 PM
macabre
Where do you then go from there?

I have done the first integration (with respect to y)

Which Gives

2
S exp(y/x){2x - x^2} dx
0

But i do not understand where to go from here; I have expanded to

2
S (2x)exp(y/x) - (x^2)exp(y/x) dx
0

but am lost as to how to then integrate this; am i meant to take the y value as a constant in order to give
_______2
exp(y) S (2x)exp(1/x) - (x^2)exp(1/x) dx
_______0