What is #f(x) = int cot2x dx# if #f(pi/8) = 0 #? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer sjc Nov 29, 2016 #f(x)=1/2lnsqrt2sin(2x)# Explanation: #f(x)=intcot2xdx# #f(x)=int((cos2x)/(sin2x))dx# now#""(d/(dx)(sin2x)=2cos2x)# we have a log integration. #f(x)=int((cos2x)/(sin2x))dx=1/2lnsin2x+C# #f(pi/8)=0# #:.1/2lnsin(pi/4)+C=0# rewrite #C=1/2lnK" "#in order to include it in the log. #1/2lnsin(pi/4)+1/2lnk=0# #1/2[(lnsin(pi/4)+lnk]=0# #1/2(lnksin(pi/4))=0# #lnx=0=>x=1# #:. ksin(pi/4)=1# #k(sqrt2/2)=1# #k=2/sqrt2=sqrt2# #f(x)=1/2lnsqrt2sin(2x)# 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 1523 views around the world You can reuse this answer Creative Commons License