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Question

Let f:RR be a continuous function which satisfies f(x)=x0f(t)dt. Then the value of f(loge5) is

A
0 (Zero)
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B
2
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C
5
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D
3
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Solution

The correct option is A 0 (Zero)
f(x)=x0f(t)dt (1)
Differentiate the above equation, ddxf(x)=ddxx0f(t)dt
Using Newton-Leibnitz's rule, we get
f(x)=f(x)×10=f(x)
f(x)=Aex where A is constant.

From (1), we get
f(0)=0A=0
f(x)=0, xR
f(loge5)=0

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