Hello, I must be having some sort of brain malfunction or something. First here is my question: Evaluate the line integral with respect to arc length The integral sub C of x*e^y ds where C is the arc of the unit circle from (1,0) to (-1,0) traversed counterclockwise. Now if the circle is traversed counterclockwise then -1 <= x <= 1 and 0 <= y <= 1. I can parameterize the equation by noticing that x = cos theta and y = sin theta. Therefore the integral becomes The integral of cos theta * e^sin theta ds where ds is ( (-sin theta)^2 + (cos theta)^2 )^1/2 = 1 So the integral becomes The integral of cos theta * e^sin theta dtheta. Since the unit circle is traversed counterclockwise the angle goes from 0 to pi. If I let sin theta = u then du = cos theta and the limits become zero and zero. So if I integrate the integral of e^u du then I get e^u with the limits of 0 and 0 which ends up to be zero. This cannot be right can it? I am confused. I think I did everything correctly. Where am I going wrong? Perhaps I am right? Any help is appreciated. Thankyou.