Chapter 14.2, Problem 17E

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.

17.     ${\displaystyle \underset{C}{\int }\frac{x}{x^2+y^2}}ds;$ C is the line segment from (1, 1) to (10, 10).