Mathematics

Find the integral 
1) $$\int {\dfrac{{dx}}{{\sqrt {9 - 25{x^2}} }}} $$


SOLUTION
Sol :- $$\displaystyle \int \dfrac{dx}{\sqrt{9-25x^{2}}} = \frac{1}{5}\int \frac{1}{\sqrt{\left ( \dfrac{3}{5} \right )-x^{2}}} $$
Using $$\displaystyle \int \frac{1}{\sqrt{a^{2}-x^{2}}} = sin^{-1}\frac{x}{a}+c $$
$$\displaystyle = I = \frac{1}{5}\int \frac{1}{\sqrt{\left ( \dfrac{3}{5} \right )^{2}-x^{2}}} = \frac{1}{5}sin ^{-1}\frac{5x}{3}+c $$
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Subjective Medium Published on 17th 09, 2020
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