What is f(x) = int cot2x dx if f(pi/8) = 0 ?

1 Answer
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)