# The cost function for a product is C(x)=0.8x^2 +120x+110. How to find average cost over [0,600] ?

## .

Mar 5, 2016

${C}_{a v g} = \overline{C} = \frac{1}{600} {\int}_{0}^{600} C \left(x\right) \mathrm{dx} = 132110$

#### Explanation:

The average cost over this interval may be given by

${C}_{a v g} = \frac{1}{600 - 0} {\int}_{0}^{600} C \left(x\right) \mathrm{dx}$

$= \frac{1}{600} {\int}_{0}^{600} \left(0.8 {x}^{2} + 120 x + 110\right) \mathrm{dx}$

$= \frac{1}{600} {\left[\frac{0.8 {x}^{3}}{3} + \frac{120 {x}^{2}}{2} + 110 x\right]}_{0}^{600}$

$= \frac{1}{600} \left[57600000 + 21600000 + 66000 - 0\right]$

$= 132110$.