Choose the correct answer-1-9 x-4 x2 d x equals tob frac 12sin-1 veft lfrac8 x-99 right -C

∫1/√(9x 4x^2)dx =1/√(4)∫1/√(9/4x x^2) 1/2∫1/√( [ x^2 9/4x+(9/8)^2 ]+(9/8)^2)dx =1/2∫1/√((9/8)^2 (x 9/8)^2)dx =1/2sin^ 1 ( x 9/8/9/8 )+C [ ∵∫dx/√(a^2 x^2)=s ...

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Byju's Answer

Standard XII

Mathematics

Integration Using Substitution

Choose the co...

Question

Choose the correct answer.
$\int \frac{1}{9 x - 4 x^{2}} d x$ equals to
$(a) \frac{1}{9} s i n^{- 1} (\frac{9 x - 8}{8}) + C (b) \frac{1}{2} s i n^{- 1} (\frac{8 x - 9}{9}) + C (c) \frac{1}{3} s i n^{- 1} (\frac{9 x - 8}{8}) + C (d) \frac{1}{2} s i n^{- 1} (\frac{9 x - 8}{9}) + C$

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Solution

$\int \frac{1}{\sqrt{9 x - 4 x^{2}}} d x = \frac{1}{\sqrt{4}} \int \frac{1}{\sqrt{\frac{9}{4} x - x^{2}}} \frac{1}{2} \int \frac{1}{\sqrt{- [x^{2} - \frac{9}{4} x + (\frac{9}{8})^{2}] + (\frac{9}{8})^{2}}} d x = \frac{1}{2} \int \frac{1}{\sqrt{(\frac{9}{8})^{2} - (x - \frac{9}{8})^{2}}} d x = \frac{1}{2} s i n^{- 1} (\frac{x - \frac{9}{8}}{\frac{9}{8}}) + C [∵ \int \frac{d x}{\sqrt{a^{2} - x^{2}}} = s i n^{- 1} (\frac{x}{a})] = \frac{1}{2} s i n^{- 1} (\frac{8 x - 9}{9}) + C$
Hence, the option (b)is correct.

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Similar questions

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Choose the correct answer in the given question.
$\int \sqrt{1 + x^{2}} d x$ is equal to
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Q. If

\frac{1}{^{5} C_{r}} + \frac{1}{^{6} C_{r}} = \frac{1}{^{4} C_{r}},

then the value of

r

equals to

Choose the correct answer in each of the question.
$\int \frac{d x}{x (x^{2} + 1)}$ equals
$(a) l o g | x | - \frac{1}{2} l o g (x^{2} + 1) + C (b) l o g | x | + \frac{1}{2} l o g (x^{2} + 1) + C (c) - l o g | x | + \frac{1}{2} l o g (x^{2} + 1) + C (d) \frac{1}{2} l o g | x | + l o g (x^{2} + 1) + C$

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Choose the correct answer. ∫19x−4x2dx equals to (a)19sin−1(9x−88)+C(b)12sin−1(8x−99)+C(c)13sin−1(9x−88)+C(d)12sin−1(9x−89)+C

∫1√9x−4x2dx=1√4∫1√94x−x212∫1√−[x2−94x+(98)2]+(98)2dx=12∫1√(98)2−(x−98)2dx=12sin−1(x−9898)+C[∵∫dx√a2−x2=sin−1(xa)]=12sin−1(8x−99)+C Hence, the option (b)is correct.

Choose the correct answer.
$\int \frac{1}{9 x - 4 x^{2}} d x$ equals to
$(a) \frac{1}{9} s i n^{- 1} (\frac{9 x - 8}{8}) + C (b) \frac{1}{2} s i n^{- 1} (\frac{8 x - 9}{9}) + C (c) \frac{1}{3} s i n^{- 1} (\frac{9 x - 8}{8}) + C (d) \frac{1}{2} s i n^{- 1} (\frac{9 x - 8}{9}) + C$