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

Let f(x)=∫ dx/(3+4x²)√(4-3x²), |x|<2/√3. If f(0)=0 and f(1)=1/αβt… | JEE Main 2023 Mathematics PYQ

NVAMediumJEE Main 2023 · 15 April, Shift 1Integration Techniques (Substitution, Parts, Partial Fractions)

Let $f(x)=\int \frac{dx}{(3+4x^2)\sqrt{4-3x^2}},\quad |x|<\frac{2}{\sqrt{3}}.$ If $f(0)=0$ and $f(1)=\frac{1}{\alpha\beta}\tan^{-1}\!\left(\frac{\alpha}{\beta}\right), \quad \alpha,\beta>0,$ then $\alpha^2+\beta^2$ is equal to

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