Using fundamental Theorem on line intehrals to evaluate $\displaystyle \int_{C}F(x,y)dS,$ where $C$ is any path from $(1,1)$ to $(2,6)$ and $\displaystyle F=\bigg<3y^2-\frac{5}{y},6xy+\frac{5x}{y^2}\bigg>$
What i try: First i convert the line passing through $(1,1)$ to $(2,6)$ as
$r(t)=(1-t)<1,1>+(t)<2,6>=<(1-t),(1-t)>+<2t,6t>=<1+t,1+5t>$
So parametric coordinate as $x=1+t$ and $y=1+5t$ where $0\leq t\leq 1$
So $\displaystyle dS=\sqrt{\bigg(\frac{dx}{dt}\bigg)^2+\bigg(\frac{dy}{dt}\bigg)^2}dt=\sqrt{1^2+5^2}dt=\sqrt{26}dt$
Now i put paramatric coordonate in
$\displaystyle F=\bigg<3y^2-\frac{5}{y},6xy+\frac{5x}{y^2}\bigg>$
$\displaystyle F=\bigg<3(1+5t)^2-\frac{5}{(1+5t)},6(1+t)(1+5t)+\frac{5(1+t)}{(1+5t)^2}\bigg>$
How do i solve it after that . Help me please