# What is the net area between f(x)=tanx in x in[0,pi/3]  and the x-axis?

May 8, 2016

$A = {\int}_{0}^{\frac{\pi}{3}} \tan x \mathrm{dx} = {\left[\log \left(\left\mid \sec \left(x\right) \right\mid\right)\right]}_{0}^{\frac{\pi}{3}} \approx 0.693$

#### Explanation:

GIven : $f \left(x\right) = \tan x : \to x \in \left[0 , \frac{\pi}{3}\right]$

Required : Area under $f \left(x\right) \text{ and the " x " axis}$

Solution: Straight integration of $f \left(x\right)$ in the interval $\left[0 , \frac{\pi}{3}\right]$

$A = {\int}_{0}^{\frac{\pi}{3}} \tan x \mathrm{dx} = {\left[\log \left(\left\mid \sec \left(x\right) \right\mid\right)\right]}_{0}^{\frac{\pi}{3}} \approx 0.693$