QJEEM23Ma62da: JEE Main 2023 Mathematics - Class 12 JEEM23Ma62da Solution: Let be the area of the larger region bounded by the curve and…

${A_1} = \int\limits_0^2 {2\sqrt 2 \sqrt x - xdx}$

$= \left. {2\sqrt 2 \times {2 \over 3}\,.\,{x^{{3 \over 2}}} - {{{x^2}} \over 2}} \right]_0^2$

$= {{4\sqrt 2 } \over 3} \times 2\sqrt 2 - 2$

$= {{16} \over 3} - 2 = {{10} \over 3}$

${A_2} = \left. {\int\limits_2^8 {2\sqrt 2 \sqrt x - xdx = {{4\sqrt 2 } \over 3}\,.\,{x^{{3 \over 2}}} - {{{x^2}} \over 2}} } \right]_2^8$

$= {{4\sqrt 2 } \over 3}(16\sqrt 2 - 2\sqrt 2 ) - 30$

$= {{112} \over 3} - 30 = {{22} \over 3}$

{A_2} > {A_1} \Rightarrow 3\alpha = 22