{dx}{{9x-4x²} equals - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Choose the correct answer in Exercises 109 and 110.

Question : 110 of 271

Marks: +1, -0

\int\frac{dx}{\sqrt{9x-4x^2}}

equals

Solution:

Let

\int\frac{dx}{\sqrt{9x-4x^2}}

=\frac{1}{2}\int\frac{dx}{\sqrt{-x^2+\frac{9}{4}x}}

=\frac{1}{2}\int\frac{dx}{\sqrt{-\left(x^2-\frac{9}{4}x\right)}}

=\frac{1}{2}\int\frac{dx}{\sqrt{\left(\frac{9}{8}\right)^2-\left(x-\frac{9}{8}\right)^2}}

=\frac{1}{2}\sin^{-1}\left(\frac{x-\frac{9}{8}}{\frac{9}{8}}\right)+C

=\frac{1}{2}\sin^{-1}\left(\frac{8x-9}{9}\right)+C

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