Chapter 14.2, Problem 37E

Line integrals of vector fields in the plane Given the following vector fields and oriented curves C, evaluate ${\displaystyle \underset{C}{\int }F\cdot Tds}$.

37.     $F=\frac{\langle x,y\rangle }{{\left(x^2+y^2\right)}^{3/2}}$ on the curve $r\left(t\right)=\langle t^2,3t^2\rangle$, for 1 ≤ t ≤ 2