{1}{{9-25x²} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.4
Integrate the functions in Exercises 86 to 108.

Question : 89 of 271

Marks: +1, -0

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

Solution:

Let

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

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

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

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

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

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