Chapter 17.2, Problem 63E

To determine

(a)

To show:

That $F\left(r,\theta \right)=r^{-1}\langle \sin \theta ,\cos \theta \rangle$

To determine

(b)

To show:

That $F\Vert r\text{'}\left(\theta \right)\Vert d\theta =d\theta$

To determine

(c)

To show:

The integral ${\displaystyle {\int }_C\left(x^2-y^2\right)ds}$ for the semicircle given.