# What is the average value of a function y=7 sin x on the interval [0,pi]?

Dec 21, 2016

The answer is $= \frac{14}{\pi}$

#### Explanation:

The average value of a function $y = f \left(x\right)$ from $x = a$ to $x = b$ is

$\overline{y} = \frac{{\int}_{a}^{b} f \left(x\right) \mathrm{dx}}{b - a}$

Therefore,

$\overline{y} = \frac{{\int}_{0}^{\pi} 7 \sin x \mathrm{dx}}{\pi - 0}$

$= \frac{7}{\pi} {\left[- \cos x\right]}_{0}^{\pi}$

$= \frac{7}{\pi} \left[1 + 1\right]$

$= \frac{14}{\pi}$