Chapter 15, Problem 7RE

Assume that C is the parametric curve $x=x\left(t\right),y=y\left(t\right),$ where t varies from a to b. In each part, express the line integral as a definite integral with variable of integration t.

$\begin{array}{l}\left(\text{a}\right){\displaystyle {\int }_{C}f\left(x,y\right)dx+g\left(x,y\right)dy}\\ \left(\text{b}\right){\displaystyle {\int }_{C}f\left(x,y\right)ds}\end{array}$