How do you solve this difficult calculus problem?
Let C be the path counterclockwise around the circle given by x^2 + y^2 = 16.
Then if f(x, y) = (sin x)(cosh y) and g(x, y) = (-cos x)(sinh y), how would you evaluate the integral...
∫ f(x, y) dx + g(x, y) dy
C
which of these is the correct response?
a. 4π
b. 6π
c. 8π
d. 0
e. -4π
f. -6π
g. -8π
h. none of these
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Verified answer
You have to use Green's theorem
∫ f(x, y) dx + g(x, y) dy
C
= ∫ [gx - fy] * dA
gx = sinx sinhy
fy = sinx sinhy
So the answer is 0.
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