First slide

Introduction to definite integration

Question

$\int_{π / 2}^{3 π / 2} \frac{1}{1 + \cos x} d x$

Moderate

A

2
B

$- 2$
C

$\frac{1}{2}$
D

$- \frac{1}{2}$

Solution

$\begin{array}{l} G.I = \int_{π / 2}^{3 π / 2} \frac{1}{2 \cos^{2} \frac{x}{2}} d x = \frac{1}{2} \int_{π / 2}^{3 π / 2} \sec^{2} \frac{x}{2} d x \\ = \frac{1}{2} {[2 \cdot \tan \frac{x}{2}]}_{π / 2}^{3 π / 2} \\ = \tan \frac{3 π}{4} - \tan \frac{π}{4} \\ = - 1 - 1 = - 2 \end{array}$

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