Finding the area in calculus?

Find the area under the curve y = 1/Inx from x = 2 to 5

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  • Ian H
    Lv 7
    6 months ago

    ∫[1/ln(x)]dx has no simple function form

    If you just require a value for

    I ={x: 2 to 5)} ∫[1/ln(x)]dx it is ~ 2.58942453 (graphic calculator)

    Wolfram Alpha gives it as Li(5) – Li(2) where

    Li represents a special function, the logarithmic integral. It gives good approximation to the prime-counting function, and if you scroll down to series in this link you can find a rapidly convergent series equivalent due to Ramanujan.

    https://en.wikipedia.org/wiki/Logarithmic_integral...

  • 6 months ago

    Google "logarithmic integral calculator" and

    select the keisan.casio.com link,

    to find li(5) and li(2),

    then subtract li(5) - li(2) to get the answer.

    A one-trapezoid use of the trapezoidal rule gives around 3.1;

    three trapezoids gives 2.66;

    six trapezoids gives 2.61;

    lots and lots of trapezoids will get close to 2.58

  • 6 months ago

    X=2(x) + 2(y) ghjiugnkijn

  • ?
    Lv 6
    6 months ago

    Doesn't 1/ln(x) integrate into something really nice like e? I think it takes u-sub. Been a billion years since grammar school.

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  • 6 months ago

    You already asked this and it had answers:

    https://answers.yahoo.com/question/index?qid=20190...

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