If $\int_{- 1/2}^{1/2}{\cos{x\log\left( \frac{1 + x}{1 - x} \right)dx = k.\log 2}}$, then $k$ equals

Question

Dr. Abubacker · Accepted Answer

(a)
$\cos\ x\ \log\left( \frac{1 + x}{1 - x} ight)$is an odd function
$	herefore\ \int_{- 1/2}^{1/2}{\cos{x\log\ \left( \frac{1 + x}{1 - x} ight)dx = 0}}$
$	herefore\ k = 0$

Q. If $\int_{- 1/2}^{1/2}{\cos{x\log\left( \frac{1 + x}{1 - x} \right)dx = k.\log 2}}$, then $k$ equals

Explanation

Reviewed by Dr. Abubacker

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