Answer
$k[\dfrac{1}{2}-\dfrac{1}{\sqrt{30}}]$
Work Step by Step
Work done$W=\int_C F\cdot dr=\int_0^{1} \dfrac{k}{(4+26t^2)^{3/2}}\lt 2,t,5t \gt \cdot \lt 0, 1,5 \gt dt$
$=\int_0^{1} \dfrac{k(t+25t)}{(4+26t^2)^{3/2}}dt$
$=(\dfrac{1}{2}) \int_0^{1} \dfrac{k \times (52t)}{(4+26t^2)^{3/2}}dt$
Use $4+26 t^2=t ;dt=52 t dt$
$=(k/2) \int_4^{30} \dfrac{dt}{t^{3/2}}$
$=[\dfrac{k}{2}]\dfrac{-2}{p^{1/2}}]_4^{30}$
$=k[\dfrac{1}{2}-\dfrac{1}{\sqrt{30}}]$
