QJEEM24Macc34: JEE Main 2024 Mathematics - Class 12 JEEM24Macc34 Solution: The area of the region is

\begin{aligned}& y^2 \leq 4 x, x<4 \\& \frac{x y(x-1)(x-2)}{(x-3)(x-4)}>0 \\& \text { Case - I}: y>0 \\& \frac{x(x-1)(x-2)}{(x-3)(x-4)}>0 \\& x \in(0,1) \cup(2,3) \\& \text { Case }- \text { II : y<0 } \\& \frac{x(x-1)(x-2)}{(x-3)(x-4)}<0, x \in(1,2) \cup(3,4)\end{aligned}

$$\begin{array}{rl}& \text{ Area }=2\underset{0}{\overset{4}{\int }}\sqrt{x}dx\\ & =2\cdot \frac{2}{3}{\left[x^{3/2}\right]}_0^4=\frac{32}{3}\end{array}$$