If ∫_(-π/2)^(π/2) (96x² cos² x)/(1 + e^x) dx = π(aπ² + β), a, β ∈… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 28 January, Shift 1Properties of Definite Integrals

If $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^2 \cos^2 x}{1 + e^x} dx = \pi(a\pi^2 + \beta), \quad a, \beta \in \mathbb{Z}$ , then $(a + \beta)^2$ equals:

A
$100$
B
$64$
C
$144$
D
$196$

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