Use Green's Theorem to evaluate the line integral along the given positively oriented curve.
C
2y + 8e
x
dx +
11x + 4 cos(y2)
dy
C is the boundary of the region enclosed by the parabolas
y = x2 and x = y2
Step 1
We note that C is a positively-oriented, smooth, simple closed curve. Green's Theorem tells us that in this situation, if D is the region bounded by C, then
P dx + Q dyC
=
∂Q∂x
−
∂
3
∂y
dA.D