# How do you evaluate the integral int tan theta d(theta) from 0 to pi/2?

Jul 7, 2016

integral non convergent :-(

#### Explanation:

${\int}_{0}^{\frac{\pi}{2}} d \theta \tan \theta$

$= {\int}_{0}^{\frac{\pi}{2}} d \theta \sin \frac{\theta}{\cos} \theta$

and because $\frac{d}{\mathrm{dx}} \ln f \left(x\right) = \frac{1}{f} \left(x\right) f ' \left(x\right)$

$= - {\left[\ln \cos \theta\right]}_{0}^{\frac{\pi}{2}}$

$= {\left[\ln \cos \theta\right]}_{\frac{\pi}{2}}^{0}$

$= \left[\ln \cos 0\right] - \left[\ln \cos \left(\frac{\pi}{2}\right)\right]$

$= \left[\ln 1\right] - \left[\textcolor{red}{\ln 0}\right]$