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Math Help - Estimating ln(2) using integration

  1. #1
    Member WhoCares357's Avatar
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    Estimating ln(2) using integration

    Problem:
    Estimate ln(2) using the Definition 6.9.1 (i'll show it later) and
    a) left endpoint approximation with n=2
    b) right endpoint approximation with n=2

    Defintion 6.9.1:
    \int_(e^n)^1 1/t dt = n<br />
\int_(e^n)^1 1/t dt = ln(e^n)<br />
\int_x^1 1/t dt = ln(x)

    edit: I'm still new to the latex system.
    Integration from 1 to e^n (1/t)dt = n
    Integration from 1 to e^n (1/t)dt = e^n
    Integration from 1 to x (1/t)dt = ln(x)
    Last edited by WhoCares357; August 30th 2009 at 09:29 AM.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    \ln{2} = \int_1^2 \frac{1}{t} \, dt \approx<br />

    left sum ...

    \frac{2-1}{2} \left(1 + \frac{2}{3}\right)

    right sum ...

    \frac{2-1}{2} \left(\frac{2}{3} + \frac{1}{2}\right)
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