What is #f(x) = int 1/(x-4) # if #f(2)=1 #? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer maganbhai P. Jun 21, 2018 #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)# Answer link Related questions How do you find the constant of integration for #intf'(x)dx# if #f(2)=1#? What is a line integral? What is #f(x) = int x^3-x# if #f(2)=4 #? What is #f(x) = int x^2+x-3# if #f(2)=3 #? What is #f(x) = int xe^x# if #f(2)=3 #? What is #f(x) = int x - 3 # if #f(2)=3 #? What is #f(x) = int x^2 - 3x # if #f(2)=1 #? What is #f(x) = int 1/x # if #f(2)=1 #? What is #f(x) = int 1/(x+3) # if #f(2)=1 #? What is #f(x) = int 1/(x^2+3) # if #f(2)=1 #? See all questions in Evaluating the Constant of Integration Impact of this question 2058 views around the world You can reuse this answer Creative Commons License