Engineering Board Exam Reviewer · Vector Calculus: Gradient, Divergence, and Curl · hard

Evaluate C(x,dy-y,dx) counterclockwise around the circle x2+y2=4.

  1. 12.57
  2. 50.27
  3. 0
  4. 25.13

Answer

D. 25.13

Solution

By Green's theorem, (M,dx+N,dy)= ≤ft( N/ x- M/ y )dA with M=-y, N=x. The integrand is 1-(-1)=2, so the integral is 2·( area)=2π(2)2=8π 25.13.

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