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Question

# Assertion :If f(x)=∫x1lntdt1+t+t2(x>0) then f(x)=−f(1x) Reason: If f(x)=∫x1lntdtt+1, then f(x)+f(1x)=12(lnx)2

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is incorrect but Reason is correct
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D
Both Assertion and Reason are incorrect
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Solution

## The correct option is C Assertion is incorrect but Reason is correctf(1x)=∫1x1logt1+t+t2dtSubstitute t=1z⇒dt=−1z2dz∴f(1x)=∫x1log1z1+1z+1z2(−dzz2)=∫x1logzdzz2+z+1=∫x1logtdt1+t+t2=f(x)

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