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Math Help - fundamental theorem!!!

  1. #1
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    fundamental theorem!!!

    Use the figure below to find the following quantities.



    (a)


    (b) The average value of f(x) on the interval [1, 6].


    can i get some help with this bad flippin johnny, thanks...

    mathlete
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  2. #2
    o_O
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    (a) What does a definite integral mean? Surely you know it's the area under the curve. You know each square is 1 units^{2} in area so you can figure out what the area under the curve is.

    (b) Average value of a function over an interval [a,b] is given by:
    f_{avg} = \frac{1}{b-a} {\color{blue} \int_{a}^{b} f(x) dx}

    You are given a and b and you know found the definite integral from (a).
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  3. #3
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    Quote Originally Posted by mathlete View Post
    Use the figure below to find the following quantities.



    (a)


    (b) The average value of f(x) on the interval [1, 6].


    can i get some help with this bad flippin johnny, thanks...

    mathlete
    The integral is just the total area under the curve between 1 and 6. Area equals 8.5 if you count up the blocks.

    Average value is simply the area divided by the range or \frac{8.5}{5} = \frac{17}{10} \Rightarrow 1.7
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