- #1
wubie
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.
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.