A force $\left(3 x^2+2 x-5\right) \mathrm{N}$ displaces a body from $x=2 \mathrm{~m}$ to $x=4 \mathrm{~m}$.…
A force $\left(3 x^2+2 x-5\right) \mathrm{N}$ displaces a body from $x=2 \mathrm{~m}$ to $x=4 \mathrm{~m}$. Work done by this force is ________ $J$.
Solution
$\begin{aligned} & W=\int_{x_1}^{x_2} F d x \\ & W=\int_2^4\left(3 x^2+2 x-5\right) d x \\ & W=\left[x^3+x^2-5 x\right]_2^4 \\ & W=[60-2] J=58 J\end{aligned}$