First slide

Evaluation of definite integrals

Question

_{$\int_{0}^{π / 2} (x \sec^{2} \frac{x}{2} + 2 \tan \frac{x}{2}) d x =$}

Easy

A

_{$2 π$}
B

_$π$
C

_{$\frac{π}{2}$}
D

_{$\frac{π}{4}$}

Solution

_{$\int_{0}^{π / 2} (x \sec^{2} \frac{x}{2} + 2 \tan \frac{x}{2}) d x =$} _{$\int_{0}^{π / 2} \frac{d}{d x} (x S e c^{2} \frac{x}{2}) d x$}
_{$= {(x S e c^{2} \frac{x}{2})}_{0}^{π / 2}$}

_{$= \frac{π}{2} \times 2 - 0 = π$}

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