JEE Main202528 Jan 2025Morning ShiftMathematicsDefinite IntegrationActual

Let for some function y =f(x), ₀^x t f(t) d t=x^2 f(x), x 0 and f(2)=3 . Then f(6) is equal to

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Step-by-step solution

aligned & ₀^x t f(t) d t=x^2 f(x) & x f(x)=2 x f(x)+x^2 f^ (x) & x^2 f^ (x)=-x f(x) & f^ (x) f(x) =- 1 x & & f^ (x) f(x) d x =- 1 x d x & f(x)=- x+C & & f(2)=3 3=- 2+C & C= 6 & f(x)= 6 x f(6)=1 aligned

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