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Question

Let F(x) = f(x) + f(1x),f(x)=x1logt1+tdt. Then F(e) equals

A
12
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B
0.0
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C
1
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D
2
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Solution

The correct option is A 12
f(x)=x1logt1+tdt.(1)
f(1x)=1x1 logt1+tdt
put t=1y
dt=1y2dy(2)
Add (1) and (2)
F(e)=f(x)+f(1x)=e1 logt1+tdt+e1 logt(1+t)tdt
=e1logttdt=[(logt)22]e1=12

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