Integral closed line Integral ∫F ds where F = <y+sin(x^2), x^2 + e^y^2> and C is the circle of radius 4 centered at origin.
The Attempt at a Solution
so ds = c'(t)dt I believe...
c(t) = <4cos(t),4sin(t)>
c'(t) = <-4sin(t),4cos(t)>
Then we have
F = <y+sin^2(x),x^2+e^y^2>
y = 4sin(t)
x = 4cos(t)
F = <4sin(t)+sin^2(4cos(t)),(4cos(t))^2+e^(4sin(t))^2>
F dot c'(t) = (-16sin^2(t) - 4sin(t)*sin^2(4cos(t))) + (64(cos(t)^3)) +(e^(4sin(t))^2)*4cos(t)
and then take the integral of that with respect to dt from 0 to 2pi?