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Question

If f:RR be a continuous function such that f(x)=x12tf(t)dt, then which of the following does not hold(s) good?

A
f(π)=eπ2
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B
f(1)=e
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C
f(0)=1
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D
f(2)=2
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Solution

The correct option is D f(2)=2
f(x)=x12tf(t)dt
f(x)=ddxx12tf(t)dt
f(x)=2xf(x)
f(x)f(x)=2x
Now integrating,
f(x)f(x)=2x
lnf(x)=x2
f(x)=ex2
f(x)=e22=e4
e42.

1069068_1159934_ans_55b8a708f7b445a99cef77d21b1d725d.png

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