MathematicsMedium210×since 2002Q3316Let f be a differentiable function in (0,π2)\left( {0,{\pi \over 2}} \right)(0,2π). If ∫cosx1t2 f(t)dt=sin3x+cosx\int\limits_{\cos x}^1 {{t^2}\,f(t)dt = {{\sin }^3}x + \cos x}cosx∫1t2f(t)dt=sin3x+cosx, then 13f′(13){1 \over {\sqrt 3 }}f'\left( {{1 \over {\sqrt 3 }}} \right)31f′(31) is equal toA6−926 - 9\sqrt 26−92B6−926 - {9 \over {\sqrt 2 }}6−29C92−62{9 \over 2} - 6\sqrt 229−62D92−6{9 \over {\sqrt 2 }} - 629−6Check answerSkip