What is the average value of a function sinx on the interval [0, pi/3]?

May 3, 2016

$k = \frac{3}{2 \pi}$

Explanation:

$k = \frac{1}{b - a} {\int}_{a}^{b} f \left(x\right) d x$

$k = \frac{1}{\frac{\pi}{3}} {\int}_{0}^{\frac{\pi}{3}} \sin x d x$

$k = \frac{3}{\pi} \left[| - \cos x {|}_{0}^{\frac{\pi}{3}}\right]$

$k = \frac{3}{\pi} \left[- \cos \left(\frac{\pi}{3}\right) + \cos 0\right]$

$k = \frac{3}{\pi} \left[- \frac{1}{2} + 1\right]$

$k = \frac{3}{\pi} \cdot \frac{1}{2}$

$k = \frac{3}{2 \pi}$