calculus

Find the average rate of change of the function over the given interval. You must reduce and simplify your answer, if possible.

a. f(x)=cot x, [pi/6, pi/2]

b. f(theta)= -2 + cos (theta), [-pi, 0]

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  1. I'll tackle the first one. The second one will be left for you as an exercise.

    f(x)=cot x, [pi/6, pi/2]
    To find the average rate of change over the interval, we divide the definite integral by the interval, namely:
    Δf(x)/Δx
    =∫f(x)dx / (π/2-π/6)
    =∫cot(x)dx / (π/3)
    =[ln(sin(x))] /(π/3)
    =[0-ln(sin(π/6)]/(π/3)
    =ln(2)/π/3
    =3ln(2)/π

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