Question

integral

Answer 1

\[\int\limits_{0}^{\pi/4}\tan^-1(\tan \theta) d \theta\]

Answer 2

that is arctan(tan(theta)) right?

Answer 3

yes

Answer 4

are you there?
If not I will give you a hint:
arctan(tan(theta))=theta on that interval

Answer 5

so just integrate theta then plug in limits and subtract

Answer 6

so, completely ignore arctan and tan

Answer 7

but why

Answer 8

arctan and tan are inverse functions

Answer 9

with a certain domain of course

Answer 10

tan(x) is undefined at odd integers*pi/2
here we don't have to worry about since we are only looking at values from 0 to pi/4

Answer 11

so arctan(tan(x))=x
as long as x does not equal an odd integer times pi/2