I don't think you have done anything wrong. What makes you think that is not correct?
Hey, I am trying to solve this line integral
(2x^{3} - y^{3})dx + (x^{3} + y^{2})dy
Over C, where C is the circle of radius 1 centered at the origin, oriented counterclockwise.
So i did the equation, taking the (partial deriv of the second term with respects to x ) - (partial deriv of the first term with respects to y) and got 3x^{2} + 3y^{2}
Then converted to polar coords where 0<= r <= 1 and 0 <= Theta <= 2pi.
I changed the integrand to 3r^{2}cos^{2}(theta) + 3r^{2}sin^{2}(theta)
And the dxdy to rdrd(theta)
So the final integrand was 3r^{3}cos^{2}(theta) + 3r^{3}sin^{2}(theta) over bounds stated above
I ended up getting 3pi/2, but I dont think this is correct... Does anyone know what I did wrong?