# How do you find the average value of the function for f(x)=1+x^2, -2<=x<=2?

May 18, 2017

$\frac{7}{3}$

#### Explanation:

Average value of $f$ on $\left[a , b\right]$ is

$\frac{1}{b - a} {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$

So, for this question, the average value is

$\frac{1}{2 - \left(- 2\right)} {\int}_{-} {2}^{2} \left(1 + {x}^{2}\right) \mathrm{dx} = \frac{7}{3}$