I just need help with changing the order of integration. I can do the actually integral by myself. Thank you :)

Question

int f(x,y) dydx
where y bounds= 1 to e^x and x bounds= 0 to 4

I thought the new bounds were
int f(x,y) dxdy
x= 0 to log(y) y= 1 to e^4

Please let me know if I'm on the right track thank you:)

Answer 1

If you are finding the area bounded by y=1, y=54.6(approx), x=0, x=4, and f(x,y)=e^x, or any other one-to-one function, and if the limits for
∫e^x dydx
are y=1,f(x,y), x=0,4
then
changing the order could be:
x=e^x to 4, y=1, e^4.

However, it depends on the properties of the function, is it one-to-one, is it invertible, etc.

plot for e^x within the integration limits:
http://img829.imageshack.us/img829/1476/1291263700.png

Answer 2

Oh I see thank you
but the new bounds after you have changed the order shouldn't it be

x= log(y)to 4 --> because I rearranged the bounds from y=e^x to x=log(y)?

Answer 3

Yes, indeed. Don't understand why I didn't see it in the first place.

Answer 4

Awesome thank you :)