What is #f(x) = int (x-2)/(x-1) dx# if #f(2) = 0 #?

1 Answer
Pankaj Solanki
Sep 30, 2017

#f(x)=int(x-2)/(x-1)dx#
#f(x)=int(x-1-1)/(x-1)dx#
#f(x)=int(1+(-1)/(x-1))dx#
#f(x)=int1dx-int(1)/(x-1)dx#
#f(x)=x-log(x-1)+c#
c is constant of integration
to find the value of c we use #f(2)=0#
If #f(2)=0#
#=>2-log(2-1)+c=0#
#=>2-log1+c=0#
#=>2-0+c=0#
#=>c=-2#

Hence
#f(x)=x-log(x-1)-2#

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