1. ## another integral

I understand how the book solved the integral but don't get how they got an answer of infinity.

$\int_{0}^{\pi/2} tan x~dx=\lim_{b\to(\pi/2)^-}ln |secx|(from~0~to~b)=\infty$. I get an answer of 0. $\lim_{b\to(\pi/2)^-}[ln|secb|-ln|sec0|]=0-0=0$

What am I doing wrong?

2. Originally Posted by Possible actuary
I understand how the book solved the integral but don't get how they got an answer of infinity.

$\int_{0}^{\pi/2} tan x~dx=\lim_{b\to(\pi/2)^-}ln |secx|(from~0~to~b)=\infty$. I get an answer of 0. $\lim_{b\to(\pi/2)^-}[ln|secb|-ln|sec0|]=0-0=0$

What am I doing wrong?
$sec \left ( \frac{\pi}{2} \right ) = \frac{1}{cos \left ( \frac{\pi}{2} \right ) } \to \frac{1}{0}$
which most people take to be infinite.

-Dan