IIT-JEE 2009 · Paper 2 · Mathematics Q35

MathematicsInteger+4 / -1Question 35 of 57

Let $f:\mathbf R\to\mathbf R$ be a continuous function which satisfies
$f(x)=\int_0^xf(t)\,dt.$
Then the value of $f(\ln5)$ is

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Answer and worked solution

Official answer: 0

Differentiate. $f'(x)=f(x)$ with $f(0)=0$ (put $x=0$ ). So $f(x)=Ce^x$ with $C=0$ : $f\equiv0$ and $f(\ln5)=0$ .

Answer: 0

IIT-JEE 2009 · Paper 2, Mathematics question 35