Chapter 4.3, Problem 64E

To determine

Whether the provided statement ${\displaystyle {\int }_a^b[f\left(x\right)g\left(x\right)]}dx=\left[{\displaystyle {\int }_a^{b}f\left(x\right)dx}\right]\left[{\displaystyle {\int }_a^{b}g\left(x\right)}dx\right]$ is true or false.