First slide

Evaluation of definite integrals

Question

The value of the integral $\int_{- 1 / 2}^{1 / 2} \cos x \log (\frac{1 + x}{1 - x}) d x$ is

Moderate

A

0
B

½
C

-1/2
D

none of these

Solution

$\cos x i s e v e n a n d \log (\frac{1 + x}{1 - x}) i s o d d f u n c t i o n . H e n c e \cos x \log (\frac{1 + x}{1 - x}) i s o d d f u n c t i o n .$
$\int_{- 1 / 2}^{1 / 2} \cos x \log (\frac{1 + x}{1 - x}) d x = 0$

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