Chapter 14.2, Problem 18E

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.

18.     ${{\displaystyle \underset{C}{\int }\left(xy\right)}}^{1/3}ds;$ C is the curve y =x², for 0 ≤ x ≤ 1.