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College Calculus

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Calculate the average over the given interval. f(x)=sin(pi/x)/x^2, [1,2]

  • College Calculus - ,

    Let u = 1/x
    du = -dx/x^2

    Int(sin(pi/x)/x^2 dx)[1,2]
    = Int(-sin(pi*u) du)[1,.5]
    = 1/pi cos(pi*u) [1,.5]
    = 1/pi(cos pi/2 - cos pi)
    = 1/pi(0+1)
    = 1/pi

    Since the interval length is 1, the average is just 1/pi

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