How do you evaluate the integral int_0^(pi/4)cos(x)dx ?

Sep 25, 2014

This is a definite integral.

${\int}_{0}^{\frac{\pi}{4}} \cos \left(x\right) \mathrm{dx}$

$= {\left[\sin \left(x\right)\right]}_{0}^{\frac{\pi}{4}}$

$= \left[\sin \left(\frac{\pi}{4}\right) - \sin \left(0\right)\right]$

Use your knowledge of the unit circle to be able to evaluate $\sin$ with the values of $\frac{\pi}{4}$ and $0$.

$= \frac{\sqrt{2}}{2} - 0$

$= \frac{\sqrt{2}}{2}$

$= 0.707106781$

Note that $\frac{\pi}{4} = 0.78539816$