A simple integral with one question 
Question is: For $x$ equals $4$ and $9$, why is $t$ not $\pm2$ and $\pm3$ but just $2$ and $3$ ?

By convention, $\sqrt{a}$ represents the non-negative square root, or the principal square root, of $x$. Hence, the only case in which there are two opposite solutions is when you have $\pm\sqrt{a}$. (Note the extra $\pm$ sign.) Hence is important to note that $x = \sqrt{a}$ (one non-negative solution). should not be confused with $x^2 = a \iff \vert x\vert = \sqrt{a} \iff x = \pm\sqrt{a}$ (two solutions). So, for instance, $\sqrt{4} = \color{blue}{+}2$ and $\sqrt{9} = \color{blue}{+}3$.
