A force $F\left(x\right)=2x$ N acts on an object moved from $x=1$ m to $x=4$ m. What is the work done, expressed in SI units?

A force-position graph shows a straight horizontal line at $F=12$ N from $x=3$ m to $x=9$ m. What method is most appropriate for finding the work done over this interval?

A robotic actuator pushes a crate along a track with force $F\left(x\right)=(x^2+2x)$ N, where $x$ is in meters. How much work does the actuator do as the crate moves from $x=1$ m to $x=3$ m?

A towing mechanism exerts $F\left(x\right)=(x^2-4)$ N on a sled as it moves from $x=0$ m to $x=3$ m. What is the net work done by the mechanism?

According to the Fundamental Theorem of Calculus, if , then ${\int }_a^{b}F\left(x\right)dx$ is equal to which expression?