# integral help....?

• Jan 6th 2007, 11:01 AM
Phoebe83
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 ?
• Jan 6th 2007, 11:12 AM
CaptainBlack
Quote:

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
• Jan 6th 2007, 10:21 PM
Phoebe83
I know that COSX is antisymetric about x=pi/2 but there is tan^-1 there, what about it ?
(sorry for beeing annoying)
• Jan 7th 2007, 12:08 AM
earboth
Quote:

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
• Jan 7th 2007, 01:34 AM
CaptainBlack
Quote:

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)