Textbook Problem

In Exercises 81-86, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, explain why or give an example to show why it is false.

83. ${\displaystyle {\int }_0^{1}x\sqrt{x+1}}dx=\sqrt{x+1}{\displaystyle {\int }_0^{1}x}dx$

$=\frac{1}{2}{x}^2{\sqrt{x+1}|}_0^1=\frac{\sqrt{2}}{2}$