Evaluate the line integral, where C is the given curve.
integral of xy^4. C is the right half of the circle x^2 + y^2 =16
integral of line integral= integral of r(t) |r'(t)| dt
The Attempt at a Solution
I set up a parametric equation to be r(t)=(4cost, 4sint)
then r'(t)=(-4sint, 4cost) --> |r'(t)|=4
My t is between -pi/2 and pi/2---these are my limits of integration.
With the limits of integration, my integrand is (4)(cost)(sint)^4. Setting my u=sint, my final answer came out to be 8/5. I know I got the wrong answer though...