Q59 / 150 · MHT CET 2017 · Mathematics

If $\int \frac{1}{\sqrt{9 - 16 x^{2}}} d x = α \sin^{- 1} (β x) + c,$ then $α + \frac{1}{β} =$

Correct answer
A
$1$
B
$\frac{7}{12}$
C
$\frac{19}{12}$
D
$\frac{9}{12}$

Solution

\int \frac{1}{\sqrt{9 - 16 x^{2}}} d x = α \sin^{- 1} (β x) + c

\int \frac{1}{\sqrt{3^{2} - (4 {x)}^{2}}} d x = {\frac{1}{4} \sin}^{- 1} (\frac{4 x}{3}) + c

α = \frac{1}{4} β = \frac{4}{3}

α + \frac{1}{β} = \frac{1}{4} + \frac{3}{4} = 1

Hence, the correct answer is option: 'A'.

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