JEE Main 202315 Apr, Morning shiftMathematicsMediumIntegral Calculus369× since 2002Let f(x)=∫dx(3+4x2)4−3x2,∣x∣<23f(x)=\int \frac{d x}{\left(3+4 x^{2}\right) \sqrt{4-3 x^{2}}},|x|<\frac{2}{\sqrt{3}}f(x)=∫(3+4x2)4−3x2dx,∣x∣<32. If f(0)=0f(0)=0f(0)=0 and f(1)=1αβtan−1(αβ)f(1)=\frac{1}{\alpha \beta} \tan ^{-1}\left(\frac{\alpha}{\beta}\right)f(1)=αβ1tan−1(βα), α,β>0\alpha, \beta>0α,β>0, then α2+β2\alpha^{2}+\beta^{2}α2+β2 is equal to ____________.Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
