# Thread: Fundamental Theorem of Calculus

1. ## 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)= $\displaystyle 450-\frac{x^2}{2}$

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 $0.02 per day, fidn teh average daily holding cost (that is, the per-drum holding cost times the average daily inventory.) I have no clue how to do this. We have learned the F(b)-F(a) formula and that the derivative of the integral is the function. Thanks! 2. Originally Posted by Truthbetold Solon Container receives 450 drums of plastic pellets every 30 days. The inventory function (drums on hand as a function of days) is I9x)=$\displaystyle 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

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