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.