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