WBJEE · Maths · Definite Integration
Let \(f: R \rightarrow R\) be a continuous function which satisfies \(f(x)=\int_{0}^{x} f(t) d t .\) Then. the value of \(f\left(\log _{e} 5\right)\) is
- A 0
- B 2
- C 5
- D 3
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
Given, \(\quad f(x)=\int_{0}^{x} f(t) d t\) Using Leibnitz theorem, we get \[ f^{\prime}(x)=f(x) \Rightarrow f(x)=k e^{x} \] On putting \(x=0\), we get \(f(0)=\int_{0}^{0} f(t) d t\) \(\Rightarrow \quad k e^{0}=0\) \(\left.\because \int_{a}^{a} f(x) d x=0\right]\)…
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