How do you solve this difficult calculus problem?

Question

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

Answer 1

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.

Answer 2

My first decision would be...18 inches. My mom continuously cautioned me to circulate with my 1st instinct (decision), she'd say, "you will continuously be suitable!" And ninety 8% of the time i'm. good success!