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Calculus

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Find the average value of the function on the given interval. f(x)=6x lnx; [1,e^2]

  • Calculus -

    average value is area under the curve divided by the interval length

    what do you get?
    Use integration by parts for x lnx

  • Calculus -

    (1/e^2-1)(6x^2 lnx/2-x^2/4)
    am I on the right track?

  • Calculus -

    Integrate the function over that interval and divide the integral by e^2 - 1.

    Try integration by parts for the integral.
    Let lnx = u and dv = 6 x dx
    du = dx/x and v = 3 x^2

    Integral of f(x) dx =Integral u dv
    = uv - Integral v du
    = 3 x^2 lnx - Integral of 3x dx
    = 3x^2 lnx - (3/2)x^2

  • Calculus -

    so my answer would be 3/2 (3e^4+1)/ (e^2-1)?

  • Calculus -

    That is correct.

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