First slide

Introduction to integration

Question

$\int \frac{dx}{\sqrt{9 - 25 x^{2}}}$ is equal to

Easy

A

$\sin^{- 1} (\frac{5 x}{3}) + C$
B

$\frac{3}{2} \sin^{- 1} (\frac{5 x}{3}) + C$
C

$\frac{1}{5} \sin^{- 1} (\frac{5 x}{3}) + C$
D

None of these

Solution

$\begin{array}{l} \int \frac{dx}{\sqrt{9 - 25 x^{2}}} = \int \frac{dx}{\sqrt{25 [{(\frac{3}{5})}^{2} - x^{2}]}} = \frac{1}{5} \int \frac{dx}{\sqrt{[{(\frac{3}{5})}^{2} - x^{2}]}} \\ = \frac{1}{5} \sin^{- 1} (\frac{x}{3 / 5}) + C [∵ \int \frac{dx}{\sqrt{a^{2} - x^{2}}} = \sin^{- 1} (\frac{x}{a})] \\ = \frac{1}{5} \sin^{- 1} (\frac{5 x}{3}) + C \end{array}$

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