Question

The value of is equal to ${\int }_3^6(\sqrt{x+\sqrt{12x-36}}+\sqrt{x-\sqrt{12x-36}})dx$is equal to

• A. $6\sqrt{3}$
• B. $4\sqrt{3}$
• C. $12\sqrt{3}$
• D. $2\sqrt{3}$

Answer 1

The correct option is A $6\sqrt{3}$

${\int }_0^3(\sqrt{}sqrt(x+3)+2\sqrt{3}\sqrt{x}+\sqrt{(x+3)-2\sqrt{3}\sqrt{x}})dx{\int }_0^3\left(\right(\sqrt{x}+\sqrt{3})+(\sqrt{3}-\sqrt{x}\left)\right)dx={\int }_0^{3}2\sqrt{3}dx=6\sqrt{3}$