# Math Help - Line integral troubles

1. ## Line integral troubles

Evaluate the line integral, where C is the given curve.

C xe^y dx, C is the arc of the curve x = e^y from (1, 0) to (e^4, 4)

Here is my work, which results in some absurdly large number (comparable to the number of atoms in the visible universe) that I know cannot possibly be the answer.

I'm fairly certain I don't have to parametrize (I don't see why I should), but I did anyways. I'd get the same answer regardless. The integration was done in WolframAlpha to ensure at least that part is correct, though I obviously have an incorrect integrand.

I was going to integrate with respect to y, but I saw that "dx" in the original integral and integrated with respect to x. I tried y anyways, and still came up with a wrong answer.

Any help would be amazing.

Thanks.

2. Why would you parameterize in terms of 't' and then fail to use 't' in your limits of integration?

It seems to me that your off-handed discarding of the parameterization ("not even needed") and your casual use of 'x' for limits may be misguided.

Try t in [0,4] You may notice that this is [ln(e^0),ln(e^4)]. If you examine the relationship between x and t, this should be the relationship.

3. Hm... I was following an example of the book, where they simply left x in terms of y and used y=y instead of y=t, but I may be mistaken about it's significance.

Regardless, I still don't think I fully understand what I'm doing here, mainly in terms of the integration limits (which I am sure is what is giving me the wrong answer).. here's my latest attempt that once again revealed an incorrect answer.

EDIT:

Okay, I got it.