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 1583 views around the world You can reuse this answer Creative Commons License