The correct option is B 12sin^ 1(8x 99)+C Let =∫dx√( 4(x^2 94x)) =12∫dx√( [x^2 94x (98)^2]) =12∫dx√((98)^2 (x 98)^2) =12sin^ 1(8x 99)+C ...

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Integration of Irrational Algebraic Fractions - 2

Solve ∫dx√9...

Question

Solve $\int \frac{d x}{\sqrt{9 x - 4 x^{2}}} d x$

\frac{1}{2} s i n^{- 1} (\frac{8 x - 1}{9}) + C

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\frac{1}{2} s i n^{- 1} (\frac{x - 9}{9}) + C

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\frac{1}{2} s i n^{- 1} (\frac{8 x - 9}{9}) + C

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Solution

The correct option is B $\frac{1}{2} s i n^{- 1} (\frac{8 x - 9}{9}) + C$
Let
$= \int \frac{d x}{\sqrt{- 4 (x^{2} - \frac{9}{4} x)}}$
$= \frac{1}{2} \int \frac{d x}{\sqrt{- [x^{2} - \frac{9}{4} x - (\frac{9}{8})^{2}]}}$
$= \frac{1}{2} \int \frac{d x}{\sqrt{(\frac{9}{8})^{2} - (x - \frac{9}{8})^{2}}}$
$= \frac{1}{2} s i n^{- 1} (\frac{8 x - 9}{9}) + C$

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