# Fundamental Theorem of Calculus

• Mar 9th 2008, 09:30 PM
Truthbetold
Fundamental Theorem of Calculus
Solon Container receives 450 drums of plastic pellets every 30 days. The inventory function (drums on hand as a function of days) is I9x)= $450-\frac{x^2}{2}$

A. Find the average daily inventory (that is, the average value of I(x) for the 30-day period)

B. If the holding cost for one drum is $0.02 per day, fidn teh average daily holding cost (that is, the per-drum holding cost times the average daily inventory.) I have no clue how to do this. We have learned the F(b)-F(a) formula and that the derivative of the integral is the function. Thanks! • Mar 9th 2008, 09:53 PM TheEmptySet Quote: Originally Posted by Truthbetold Solon Container receives 450 drums of plastic pellets every 30 days. The inventory function (drums on hand as a function of days) is I9x)= $450-\frac{x^2}{2}$ A. Find the average daily inventory (that is, the average value of I(x) for the 30-day period) B. If the holding cost for one drum is$0.02 per day, fidn teh average daily holding cost (that is, the per-drum holding cost times the average daily inventory.)

I have no clue how to do this.
We have learned the F(b)-F(a) formula and that the derivative of the integral is the function.

Thanks!

The average of a function on an interval [a,b] is given by the fomula

$A=\frac{1}{b-a}\int_a^bf(x)dx=\frac{1}{30-0}\int_{0}^{30}(450-\frac{x^2}{2})dx$