# Thread: integral help....?

1. ## integral help....?

I tried to understand a solution of an integral here: (the first)
http://www.mathhelpforum.com/math-he...integrals.html

why this integral is ZERO ?

2. Originally Posted by Phoebe83
why this integral is ZERO ?

$\displaystyle \int_0^{\pi} \tan^{-1}(\cos(x))dx$
Because the integrand is antisymetric about $\displaystyle x=\pi/2$.

RonL

3. I know that COSX is antisymetric about x=pi/2 but there is tan^-1 there, what about it ?
(sorry for beeing annoying)

4. Originally Posted by Phoebe83
I know that COSX is antisymetric about x=pi/2 but there is tan^-1 there, what about it ?
(sorry for beeing annoying)
Hello Phoebe,

I've attached a diagram of your function. You'll notice that it is antisymmetric as CaptainBlack stated.
In the drawing the value of the integral is called a.

EB

5. Originally Posted by Phoebe83
I know that COSX is antisymetric about x=pi/2 but there is tan^-1 there, what about it ?
(sorry for beeing annoying)
cos(x) is anti-symmetric about pi/2, and tan^-1 is antisymnetric about 0,
which is what we need to conclude that the composite function is anti-
symmetrix about pi/2, since cos(x) maps pi/2 to 0.

RonL