# Thread: Last math problem for test

1. ## Last math problem for test

Here it goes
∫ from 0 to 2π/3 tan (x/2) dx

this is my last problem i need to know for my test on friday so please help me out

$\int \tan{u} \, du = -\ln|\cos{u}| + C$

3. $\int_0^{\frac{2\pi}{3}} \tan\left(\frac{x}{2}\right) \, dx$

$u = \frac{x}{2}$

$du = \frac{1}{2} dx$

substitute and reset the limits of integration ...

$2 \int_0^{\frac{2\pi}{3}} \tan\left(\frac{x}{2}\right) \, \frac{1}{2}dx$

$2 \int_0^{\frac{\pi}{3}} \tan(u) \, du$

integrate ...

$2\left[-\ln|\cos{u}|\right]_0^{\frac{\pi}{3}}$

use the FTC ...

$2\left[-\ln\left(\frac{1}{2}\right) + \ln(1)\right] = 2\ln(2)$