$\int_{- π}^{π} \frac{2 x (1 + s i n x)}{1 + c o s^{2} x} d x =$

\frac{π^{2}}{4}

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π^{2}

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\frac{π}{2}

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Solution

The correct option is B $π^{2}$
$I = 4 \int_{0}^{π} \frac{x s i n x}{1 + c o s^{2} x} d x = 4 \int_{0}^{4} \frac{(π - x) s i n x}{1 + c o s^{2} x} d x ∴ 2 I = 4 π \int_{0}^{π} \frac{s i n x}{1 + c o s^{2} x} d x = 8 π \int_{0}^{π / 2} \frac{s i n x}{1 + c o s^{2} x} d x = 2 π^{2} ∴ I = π^{2}$

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