First slide

Methods of integration

Question

$\int \cos [2 \cot^{- 1} \sqrt{\frac{1 - x}{1 + x}}] dx$ is equal to

Moderate

A

$\frac{1}{2} x^{2} + C$
B

$\frac{1}{2} \sin [2 \cot^{- 1} \sqrt{\frac{1 - x}{1 + x}}] + C$
C

$- \frac{1}{2} x^{2} + C$
D

$\frac{1}{2} x + C$

Solution

$\begin{matrix} \int \cos [2 \cot^{- 1} \sqrt{\frac{1 - x}{1 + x}}] dx = \int \cos [\cos^{- 1} (- x)] dx \\ = \int (- x) dx = - \frac{x^{2}}{2} + C \end{matrix}$

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