Statement-1: If f(x)=int_(1)^(x)(log_(e )t)/(1+t+t^(2))dt, then f(x)=f((1)/(x))for all x gr 0. Statement-2:If f(x)=int_(1)^(x)(log_(e )t)/(1+t)dt, then f(x)+f((1)/(x))=((log_(e )x)^(2))/(2)

Statement-1: If f(x)=int_(1)^(x)(log_(e )t)/(1+t+t^(2))dt, then f(x)=

1.	Statement-1: If f(x)=int_(1)^(x)(log_(e )t)/(1+t+t^(2))dt, then f(x)=f((1)/(x))for all x gr 0. Statement-2:If f(x)=int_(1)^(x)(log_(e )t)/(1+t)dt, then f(x)+f((1)/(x))=((log_(e )x)^(2))/(2)
Answer» Statement-1 is true, Statement-2 is True,Statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is not a correct explanation for Statement-1. Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True. Solution :If F(X)`=underset(1)overset(x)int (log_(E )t)/(1+t+t^(2))dt`, then `f((1)/(x))=underset(1)overset(1//x)int (log_(e )t)/(1+t+t^(2))dt` `RARR f((1)/(x))=underset(1)overset(x)int (log_(e )u)/(1+u+u^(2))du`, where `t=(1)/(u)` `rArr f((1)/(x))=f(x)` So, statement-1 is true. If`f(x)=underset(1)overset(x)int (log_(e )t)/(2+t)dt`, then `((1)/(x))=underset(1)overset(1//x)int(log_(e )t)/(1+t)dt` `rArr f((1)/(x))=underset(1)overset(x)int(log_(e )u)/(u(1+u))du`, where `t=(1)/(u)` `rArr f((1)/(x))=underset(1)overset(x)int(log_(e ))/(t(l+t))dt` `:. f(x)+f((1)/(x))=underset(1)overset(x)int (log_(e )t)/(t+1)(1+(1)/(t))dt` `=underset(1)overset(x)int (logt)/(t)dt=[((log_(e )t)^(2))/(2)]_(1)^(x)=((log_(e )x)^(2))/(2)` So, statement-2 is also true.

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Statement-1: If f(x)=int_(1)^(x)(log_(e )t)/(1+t+t^(2))dt, then f(x)=f((1)/(x))for all x gr 0. Statement-2:If f(x)=int_(1)^(x)(log_(e )t)/(1+t)dt, then f(x)+f((1)/(x))=((log_(e )x)^(2))/(2)

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