First slide

Introduction to integration

Question

$\int \sqrt{\frac{1 - x}{1 + x}} d x$

Easy

A

$\sin^{2} x + \sqrt{1 - x^{2}} + C$
B

$\cos^{- 1} x - \sqrt{1 - x^{2}} + C$
C

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

$\tan^{- 1} + \sqrt{1 + x^{2}} + C$

Solution

$\begin{array}{l} \int \sqrt{\frac{1 - x}{1 + x} \frac{1 - x}{1 - x}} d x = \int \frac{d x}{\sqrt{1 - x^{2}}} + \int \frac{- x d x}{\sqrt{1 - x^{2}}} \\ = \sin^{- 1} x + \sqrt{1 - x^{2}} + C \end{array}$

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