Posted by **Taylor** on Sunday, June 5, 2011 at 5:19pm.

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]

- calculus -
**MathMate**, Sunday, June 5, 2011 at 6:04pm
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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