Example work done by variable force

A force F = 2x + 5 acts on a particle. Find the work done by the force during the displacement of the particle from x =0m to x = 2m. Given that the force is in Newtons.

Work done W = ∫F(x)dx

Thus W = = ∫F(x)dx Cos 0^o

= ∫F(x)dx

= ∫(2x + 5)dx

= 2x²/2 + 5x |

= 2² + 5 x 2

= 14 J