QJEEM21Ma99a2: JEE Main 2021 Mathematics - Class 12 JEEM21Ma99a2 Solution: The value of ∫ − π 2 π 2 ( 1 + sin 2 x 1 + π sin ⁡ x ) d x is

Question

Verified Solution • 2025–26 Session moderate

The value of

\int_{- \frac{π}{2}}^{\frac{π}{2}} (\frac{1 + \sin^{2} x}{1 + π^{\sin x}}) d x

is

Accepted Answer

I = \int_{0}^{\frac{π}{2}} \frac{(1 + \sin^{2} x)}{(1 + π^{\sin x})} + \frac{π^{\sin x} (1 + \sin^{2} x)}{(1 + π^{\sin x})} d x

I = \int_{0}^{\frac{π}{2}} (1 + \sin^{2} x) d x

I = \frac{π}{2} + \frac{π}{2} . \frac{1}{2} = \frac{3 π}{4}

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