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Math Help - integrals

  1. #1
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    Exclamation integrals

    Suppose f(x) > 0 on [2, 5].
    (1)*f(2) + (1)*f(3) + (1)*f(4) gives an estimate of the area under the graph of f.

    True or False

    Suppose f(x) > 0 on [2, 5].
    (1.5)*f(2) + (1.5)*f(5) gives an estimate of the area under the graph of f.

    True or False

    Suppose f(x) > 0 on [2, 5].
    (2)*f(3) + (1)*f(4) gives an estimate of the area under the graph of f.

    True or False




    im confused...
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by thecount View Post
    Suppose f(x) > 0 on [2, 5].
    (1)*f(2) + (1)*f(3) + (1)*f(4) gives an estimate of the area under the graph of f.

    True or False


    im confused...
    Using the definition of the Riemann sum with the left end points of each of the subdivisions.

    \Delta x=\frac{b-a}{n}=\frac{5-2}{3}=1 and

    x_i=a+i\Delta x for i=0,1,2 since we are using the left endpoints so we get

    \int_{2}^{5}f(x)dx \approx \sum_{i=0}^{2}f(x_i)\Delta x=f(2)+f(3)+f(4)

    think about the other ones and see if they fit other methods you know
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