[tex] \\ \pi \int ^3_0\left(\sqrt{3}-\sqrt{x}\right)^2 =>
\\ \boxed{u=\sqrt{3}-\sqrt{x}\right}
\\ => \int \:-2u^2\left(-u+\sqrt{3}\right)du
\\ => -2\cdot \int \:u^2\left(-u+\sqrt{3}\right)du
\\ => -2\cdot \int \:-u^3+\sqrt{3}u^2du
\\ => -2\left(-\frac{u^4}{4}+\frac{u^3}{\sqrt{3}}\right)
\\ => \boxed{Scoatem \:\ u}
\\ => \pi(-2\left(-\frac{\left(\sqrt{3}-\sqrt{x}\right)^4}{4}+\frac{\left(\sqrt{3}-\sqrt{x}\right)^3}{\sqrt{3}}\right)) |^3_0
\\ => \pi(0-\left(-\frac{3}{2}\right))
\\ => \frac{3\pi}{2}
[/tex]
