Chapter 14.2, Problem 15E

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.

15.     ${\displaystyle \underset{C}{\int }\left(x^2+y^2\right)}ds;$ C is the circle of radius 4 centered at (0, 0).