Chapter 6.4, Problem 2PT

A particle moves along an x-axis from 2 m to 3 m pushed by a force of x² N (newtons) for 2 ≤ x ≤ 3. The definite integral that determines the amount of work done is:

1. a) ${\displaystyle {\int }_2^{3}g{x}^{3}dx}$
2. b) ${\displaystyle {\int }_2^{3}xdx}$
3. c) ${\displaystyle {\int }_2^{3}2\text{π}{x}^{2}dx}$
4. d) ${\displaystyle {\int }_2^3{x}^{2}dx}$