2023 VCAA NHT Spec Exam 1 - An Interesting Integral

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  • Опубликовано: 17 окт 2024

Комментарии • 2

  • @glock8417
    @glock8417 11 месяцев назад

    A u sub of u equal to ln(ln) would have been more effective here wouldn't it?

    • @Ezallium
      @Ezallium 10 месяцев назад +2

      u = ln(lnx)
      du = 1/x * 1/lnx dx
      dx = xlnx du
      when x = e, u = ln(1) = 0
      when x = e^2, u = ln(ln(e^2)) = ln(2)
      ∫e^{e^2} (ln(lnx))/(xlnx) dx
      = ∫0^ln(2) u/(xlnx) * xlnx du
      = ∫0^ln(2) u du
      = 1/2[u^2]0^ln2
      = 1/2(ln2)^2