The value of $\int_3^6(\sqrt{x+\sqrt{12 x-36}}+\sqrt{x-\sqrt{12 x-36}}) d x$ is equal to

Question

Professor PC Thomas Classes · Answer

Simplify inner roots to form $| \sqrt{x-3} \pm \sqrt{3} |$. Integrating the resultant absolute functions yields $6\sqrt{3}$.