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Math Help - Riemann integrable

  1. #1
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    Riemann integrable

    Let f(x) = 1/x^2 when x is between [2,3)
    = 2 when x is between [3,4]


    a.) prove that f(x) is Riemann integrable on [2,4]. Given epsilon is greater than 0, find a partition P... ( i have no idea what this means. )


    b.) find a continuous funciton, F(x), statisfying F(x) = integral of f(t)dt from 2 to x on [2,4]
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  2. #2
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    [QUOTE=Nichelle14]Let f(x) = 1/x^2 when x is between [2,3)
    = 2 when x is between [3,4]


    a.) prove that f(x) is Riemann integrable on [2,4].
    Because it is countinous on this interval.
    Quote Originally Posted by Nichelle14
    Given epsilon is greater than 0, find a partition P...
    I have no idea what you mean by that. Perhaps they ask to find some partion which statisfies the Riemann integral?

    b.) find a continuous funciton, F(x), statisfying F(x) = integral of f(t)dt from 2 to x on [2,4]
    You have,
    F(x)=\int^x_2\frac{1}{t^2}dt
    Thus,
    \left -\frac{1}{t} \right|^x_2=-\frac{1}{x}+\frac{1}{2}
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