What is #f(x) = int 1/(x-4) # if #f(2)=1 #?

1 Answer
Jun 21, 2018

Answer:

#f(x)=ln|x-4|+ln(e/2)#

OR

#f(x)=ln|x-4|+1-ln2#

Explanation:

Here,

#f(x)=int1/(x-4)dx#

#f(x)=ln|x-4|+c....to(1)#

Given that ,

#f(2)=1#

#=>ln|2-4|+c=1#

#=>ln|-2|+c=1#

#=>c=1-ln2#

#=>c=lne-ln2...to[becauselne=1]#

#=>c=ln(e/2)#

Subst. #c=ln(e/2)# , into #(1)#

#f(x)=ln|x-4|+ln(e/2)#