5. Let \(\vec{F} = y \cos x \vec{i} + (\sin x + y)\vec{j}\)
a) Find a potential function for \(\vec{F}\), that is a function f such that \(\vec{F} = \nabla f\)
b) Without any parameterization of the curve C, compute \(\int_C \vec{F} \cdot d\vec{r}\) where C is the upper half of
the circle of center (2,0) and radius 4, traversed in the clockwise direction.
6. Evaluate \(\int_C (1 + \tan x)dx + (x^2 + e^y)dy\) given that C is the positively oriented boundary of the
region enclosed by the curves \(y = \sqrt{x}\), \(x = 1\) and \(y = 0\)
