If ∫0kdx/(2+18x^2)=(π)/24 , then the value of k is

Correct answer: (C) 1/3. 1/2 ∫ 0 k dx/(1+9x^2) =(π)/24 ⇒ ∫ 0 k dx/(1+( 3x )^2) =(π)/12 ⇒ ( 1/3 tan^(−1) ( 3x ) ) 0 k =(π)/12 ⇒ tan^(−1) 3k=(π)/4 ⇒ 3k=1 ⇒ k=1/3

Q61 / 150 · MHT CET 2018 · Mathematics

If $\int_{0}^{k} \frac{d x}{2 + 18 x^{2}} = \frac{π}{24}$ , then the value of $k$ is

A
$3$
B
$4$
Correct answer
C
$\frac{1}{3}$
D
$\frac{1}{4}$

Solution

\frac{1}{2} \int_{0}^{k} \frac{d x}{1 + 9 x^{2}} = \frac{π}{24}

\Rightarrow \int_{0}^{k} \frac{d x}{1 + {(3 x)}^{2}} = \frac{π}{12}

\Rightarrow {(\frac{1}{3} \tan^{- 1} (3 x))}_{0}^{k} = \frac{π}{12}

\Rightarrow \tan^{- 1} 3 k = \frac{π}{4}

\Rightarrow 3 k = 1

\Rightarrow k = \frac{1}{3}

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

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If ∫0kdx2+18x2=π24 , then the value of k is

Solution

Relevant Questions

If $\int_{0}^{k} \frac{d x}{2 + 18 x^{2}} = \frac{π}{24}$ , then the value of $k$ is