Calculus

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Hi.
In an integration solution, the integral of (1/(sqrt (8-u squared)) is written as arcsin(u/sqrt 8), but I don't see how they got it. When I did it I got (1/8)*(arcsin(u*sqrt8)). What I did was take sqrt8 common in the denominator to get it in the form sqrt(1-u sq.) and then find the integral (arcsin u) and then since my 'u' was sqrt.8 * u, I divided sqrt.8 from the whole thing. Where did I go wrong?

  • Calculus -

    "take sqrt8 common in the denominator to get it in the form sqrt(1-u sq.)"
    Shouldn't it be
    1/sqrt(8-u^2)
    =(1/sqrt(8))/(1-(u/sqrt(8))^2)


    When you do a substitution, it is always advisable to use a different letter. You are likely to confuse yourself if you use the same letter, namely, substitute u by u/sqrt(8).

    Try:
    w=u/sqrt(8)
    then
    dw=du/sqrt(8)

    and
    ∫ du/sqrt(8-u^2)
    =∫ du/(sqrt(8))/(1-(u/sqrt(8)))
    =∫ dw/(1-w^2)
    =asin(w)
    =asin(u/sqrt(8))

  • Calculus -

    square root of (1-u squared)

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