Let S = (-1, ∞) and f: S → R be defined as: f(x) = ∫₋₁^x (e^t - 1… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 31 January, Shift 1Applications of Integrals (Area)

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

f(x) = \int_{-1}^{x} (e^t - 1)^{11} (2t - 1)^5 (t - 2)^7 (t - 3)^{12} (2t - 10)^{61} \, dt

Let $p$ be the sum of squares of the values of $x$ where $f(x)$ attains local maxima and $q$ be the sum of the values of $x$ where $f(x)$ attains local minima. Then, the value of $p^2 + 2q$ is:

A
$16$
B
$27$
C
$36$
D
$40$

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