# Thread: integration wrt y and x

1. ## integration wrt y and x

A region in the xy plane is bounded by the lines y = 1 and x= 1, and the curve $\displaystyle y = e^x$.

If the question was as above but without y=1 then I can just integrate e^x. But even then what would be the boundary values? -10 to 1. -100 to 1?

Then would I integrate with respect to y to deal with the y=1 bit. Then I would have to:

y=e^x
lny = x ie I integrate x = lny. But we haven't covered this form of integration in the course yet so I doubt if this is the correct way to go.

Maybe the solution is a lot simpler - but I can't see how to solve. Can anyone help?

Angus

2. ## Re: integration wrt y and x

Originally Posted by angypangy
A region in the xy plane is bounded by the lines y = 1 and x= 1, and the curve $\displaystyle y = e^x$.

If the question was as above but without y=1 then I can just integrate e^x. But even then what would be the boundary values? -10 to 1. -100 to 1?

Then would I integrate with respect to y to deal with the y=1 bit. Then I would have to:

y=e^x
lny = x ie I integrate x = lny. But we haven't covered this form of integration in the course yet so I doubt if this is the correct way to go.

Maybe the solution is a lot simpler - but I can't see how to solve. Can anyone help?

Angus
It's the same area as the area bounded by the function $\displaystyle \displaystyle y = e^x - 1$, the $\displaystyle \displaystyle x$ axis and $\displaystyle \displaystyle x = 1$.