Evaluating path along a circle

[xmflea]

Evaluate the line integral of f(x,y) = x+2y along C, where C is the path counterclockwise around the upper half of the unit circle


Attempt:
parametric r(t)= cos(t)i + sin(t)j 0<t<pi ds=root(1)dt

integrate from 0 to pi the function cost + 2sint, and i get -2.

correct answer is 4. i think im writing the parametric wrong or something. help?

 

[millitiz]

Your formula is correct. However, notice that it is counter clockwise
Think about your order of integration, where do you start and where do you end?

Now with that in mind, you should get 4.
(and actually I think you make some calculation mistakes, because the way you did it, you should get -4 instead of -2. Check your calculation.)