Let $f(x)=\int\frac{dx}{\left(3+4x^2\right)\sqrt{4-3x^2}}$, $|x| 0$, then $\alpha^2+\beta^2$ is equal to ______.

JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

Let

f(x)=\int\frac{dx}{\left(3+4x^2\right)\sqrt{4-3x^2}}

|x|<\frac{2}{\sqrt{3}}

. If

f(0)=0

and

f(1)=\frac{1}{\alpha\beta}\tan^{-1}\left(\frac{\alpha}{\beta}\right)

\alpha,\beta>0

, then

\alpha^2+\beta^2

is equal to ______.

Official answer

NTA final key.