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Math Help - Fundamental Theorem of Calculus

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    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!
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    Behold, the power of SARDINES!
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    Quote Originally Posted by Truthbetold View Post
    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
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