Answer
(a) $0$
b) $(h-x) \times ( \ Area \ enclosed \ inside \ the \ curve \ C)$
Work Step by Step
The tangential form for Green's Theorem is given as:
Counterclockwise Circulation: $\oint_C F \cdot T ds= \iint_{R} (\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}) dx dy $ ...(1)
a) $\oint_C f(x) dx +g(y) dy= \iint_{R} (0-0) dx dy =0$
b) $\oint_C ky dx +h(x) dy= \iint_{R} (\dfrac{h(x) }{\partial x}-\dfrac{k y}{\partial y}) dx dy $
or, $=(h-x) \iint_{R} \ dx \ dy$
or, $=(h-x) \times ( \ Area \ enclosed \ inside \ the \ curve \ C)$
