Question

फलन का समाकलन कीजिए।

${\displaystyle \frac{1}{\sqrt{9-25x^2}}}$

Answer 1

Let ${\displaystyle I=\int \frac{dx}{\sqrt{9-25x^2}}}$

${\displaystyle =\frac{1}{5}\int \frac{dx}{\sqrt{\frac{9}{25}-x^2}}}$

${\displaystyle =\frac{1}{5}\int \frac{dx}{\sqrt{{\left(\frac{3}{5}\right)}^2-x^2}}}$

${\displaystyle \frac{1}{5}{\sin }^{-1}\left(\frac{x}{\frac{3}{5}}\right)+C}$          ....${\displaystyle [\because \int \frac{dx}{\sqrt{a^2-x^2}}={\sin }^{-1} \frac{x}{a}+C]}$

${\displaystyle =\frac{1}{5}{\sin }^{-1}\left(\frac{5x}{3}\right)+C}$