question_answer

A force F is related to the position of a particle by the relation . Find the work done by the force when the particle moves from \[x=2m\] to \[x=4m\].

Answer:

                \[W=\int\limits_{2}^{4}{F\,dx}=\int\limits_{23}^{4}{10\,{{x}^{2}}\,\,dx}=\left[ \frac{10{{x}^{3}}}{3} \right]_{2}^{4}=\frac{10}{3}\left[ {{4}^{3}}-{{2}^{3}} \right]=\frac{10}{3}\times 56=186.7J\]