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Question

Let f:(0,)R and F(x)=x1f(t)dt and F(x2)=x2(1+x) then f(4) equals

A
54
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B
7
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C
4
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D
2
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Solution

The correct option is C 4
F(x)=f(x)F(x)=x(1+x)=x+x3/2F(x)=f(x)=1+32xf(4)=4

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