Answer
$94.8231$
Work Step by Step
Here,we have $ds=\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}$
or, $=\sqrt{(2t)^2+(3t^2)^2+(\dfrac{1}{2\sqrt t})^2}=\sqrt {4t^2+9t^4+(\dfrac{1}{4}) t} dt$
Now,we have $\int_{C} \overrightarrow{F} \cdot \overrightarrow{dr}=\int_1^2 (t^2) \cdot (t^3) \tan^{-1} (\sqrt t) [\sin (t^3+t^4)] \cdot \sqrt {4t^2+9t^4+\dfrac{1}{4}t} dt$
Need to use calculator.
$\int_{C} \overrightarrow{F} \cdot \overrightarrow{dr}=94.8231$
