QJEEM24Ma6aad: JEE Main 2024 Mathematics - Class 12 JEEM24Ma6aad Solution: Let S = ( − 1 , ∞ ) and f : S → R be defined as f ( x ) = ∫ − 1 …

Let $$S=(-1,\mathrm{\infty })$$ and $$f:S\to \mathbb{R}$$ be defined as

$$f(x)=\underset{-1}{\overset{x}{\int }}{(e^t-1)}^{11}(2t-1{)}^5(t-2{)}^7(t-3{)}^{12}(2t-10{)}^{61}dt\text{, }$$

Let $$\mathrm{p}=$$ Sum of squares of the values of $$x$$, where $$f(x)$$ attains local maxima on $$S$$, and $$\mathrm{q}=$$ Sum of the values of $$\mathrm{x}$$, where $$f(x)$$ attains local minima on $$S$$. Then, the value of $$p^2+2q$$ is _________.