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
(2x3 - y3)dx + (x3 + y2)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 3x2 + 3y2
Then converted to polar coords where 0<= r <= 1 and 0 <= Theta <= 2pi.
I changed the integrand to 3r2cos2(theta) + 3r2sin2(theta)
And the dxdy to rdrd(theta)
So the final integrand was 3r3cos2(theta) + 3r3sin2(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?