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Brainstorm and confusion of concepts

  1. Jan 13, 2016 #1
    I know several math formulas, like which I will write below.
    [tex] \int_{x_0}^{x_1} f(x) dx [/tex]
    [tex] \frac{\int_{x_0}^{x_1} f(x) dx}{x_1-x_0} [/tex]
    [tex] \frac{\int_{x_0}^{x_1} f(x) dx}{2} [/tex]
    [tex] f(x_1) - f(x_0) [/tex]
    [tex] \frac{f(x_1) - f(x_0)}{x_1-x_0} [/tex]
    [tex] \frac{f(x_1) - f(x_0)}{2} [/tex]
    [tex] \frac{f(x_1) + f(x_0)}{2} [/tex]
    And I know too that all equations above are importants, appears with very often. But my doubt is the following:
    My head is confused, are to much equations and concepts disconnected. I know that the inverse analog of derivative is the primitive, but what's the inverse analog of the arithmetic mean? If the AM of two numbers is (a+b)/2, so the analog inverse is (a-b)/2? And what's the inverse analog of (a+b+c)/3? What's the difference between the equations that I posted above!? What's the inverse analogo of each equation that I wrote above?
  2. jcsd
  3. Jan 13, 2016 #2


    Staff: Mentor

    None of the above is an equation, so none would be considered a formula. They are all expressions.
    Writing them as you have above is a meaningless exercise if you don't know what they represent.
    ##\int_{x_0}^{x_1} f(x) dx ## -- Could be the area under the graph of y = f(x) between x = 0 and x = 1 (depending on what the function is)
    ##\frac{\int_{x_0}^{x_1} f(x) dx}{x_1-x_0} ## -- Average value of f on the interval [0, 1]
    ##\frac{\int_{x_0}^{x_1} f(x) dx}{2} ## -- No significant meaning
    ## f(x_1) - f(x_0)## -- Vertical distance between two points on the graph of f
    ## \frac{f(x_1) - f(x_0)}{x_1-x_0}## -- Slope of the secant line between the points ##(x_0, f(x_0))## and ##(x_1, f(x_1))##
    ## \frac{f(x_1) - f(x_0)}{2}## -- No significant meaning
    ## \frac{f(x_1) + f(x_0)}{2} ## -- Average (or mean) of two function values
    None that I'm aware of.
    There's no such concept, as far as I know.
    There is none.
    Again, none of the things you posted is an equation. An equation states that two expressions are equal (i.e., has = in it).
    The question is meaningless.
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