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Math Help - area under the curve

  1. #1
    Newbie
    Joined
    May 2008
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    6

    area under the curve

    Thanks so much.
    Q1, use two rectangles to approximate the area contained between the curve and the x-axis.
    use the method indicated and give your answer correct to two decimal places.
    a, y=1/2xsquared between x=2 and x=3
    using the right end point method

    b, y=cos x between x=0 and x=pie/2
    using the left endpoint method

    c, y=1/2xcubed between x=1 and x=3
    using the right endpoint method
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  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    i'll do start the first question for you..

    y=\frac{x^2}{2} on [2,3] using right-end-point method.

    so, a_0=2, 2+ \frac{1}{n}, 2+ \frac{2}{n}, ..., 2+ \frac{n-1}{n}, 3=a_n

    I_k = \left[2+\frac{k-1}{n}, 2+\frac{k}{n}\right]

    so the area of the k^{th} rectangle is
    A_k = f\left(2+\frac{k}{n}\right) \cdot \frac{1}{n}
    ....

    do the continuation..
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