Wednesday

July 23, 2014

July 23, 2014

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

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

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

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

**Related Questions**

calculus - g(t)=2+cos t; [0,pi] Can you help me find the average rate of change ...

calculus (rate of change) - consider the function f(x)=x^2-6x+12 a. find the ...

Calulus - Consider the following function. f(t) = 3t2 − 3 (a) Find the ...

calculus - Given the function: f(x)=x^3-4x^2+6x-3 a) Find the average rate of ...

Calculus Rate of Change - Find the average rate of change h(x)=2x^2-4 from x=2 ...

Calculus - I'm supposed to find the average value of the function over the given...

math - h(t)=cos t, [pi/4, 3pi/4] find the average rate of change of the function...

Trigonometry - I don't understand how I'm supposed set the problem up or what ...

calculus - i'm not sure how to do this. can someone help, please? thanks! ...

Brief Calculus - Calculate the average rate of change of the given function ...