Chapter 14.2, Problem 19E

Scalar line integrals in the plane

a.    Find a parametric description for C in the form $r\left(t\right)=\langle x\left(t\right),y\left(t\right)\rangle .$

b.    Evaluate $\left|r^{\prime }\left(t\right)\right|$.

c.    Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.

19.     ${\displaystyle \underset{C}{\int }xy}ds;$ C is the portion of the ellipse $\frac{x^2}{4}+\frac{y^2}{16}=1$ in the first quadrant, oriented counterclockwise.