Evaluate the integral zi xyj xk dr over the circle x2 z2

Evaluate the integral (zi + xyj - xk) dr over the circle x^2 + z^2 = 9, y = 3 whose normal vector is: n = j

Solution

x = 3 cos , z = 3 sin , 0 2;

so dr = {3 sin i - 3 cos j + 3 sin k} dt.

the vector field F is given by F = 3 sin i + (3 cos . 3 . 3 sin )j - 3 cos k

Now take the dot product of F with dr and integrate from 0 to 2.