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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.

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# Homework Help: Line Integrals

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