JEE Advanced2009MathematicsDefinite IntegrationActual

Let f: R R be a continuous function, which satisfies f(x)= ₀^x f(t) d t . Then, the value of f( 5) is

Correct answer

Step-by-step solution

From given integral equation, f(0)=0 . Also, differentiating the given integral equation w.r.t. x , we get gathered f^ (x)=f(x) If f(x) 0 f^ (x) f(x) =1 f(x)=x+C f(x)=e^C e^x f(0)=0 e^C=0, a contradiction f(x)=0, x R f( 5)=0 gathered

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