Find the average value in a calculus approach

[silverbell]

Homework Statement

Find the average value of : f(x) = 4sinx + 4cosx on the interval [0, 16pi/6]

Average value: ?

Homework Equations

Integrals

The Attempt at a Solution

1/ [(16pi/6) -0] ∫ from 0 to 16pi/6 4sinx + 4cosx dx

[3/8pi] ∫ from 0 to 16pi/6 4sinx + 4cosx dx <------simplify

[3/8pi] ∫ from 0 to 16pi/6 4sinx - 4cosx <------ integrated

[3/8pi] [4sin(16pi/6) - 4cos(16pi/6)] - [3/8pi] [ 4sin(0) - 4cos(0)] <----substitution

I get 12.296 but the answer isn't right. I don't know what I'm doing wrong. Please help me understand what I'm doing wrong. Thank you very much. :)

 

[SammyS]

What did you get for 3/(8π),? (Yes, the parentheses are important.)

    "    sin(16π/6) ?

    "    cos(16π/6) ?

    "    4sin(0) - 4cos(0) ?

I would estimate that the answer is considerably smaller than 4, maybe less than 1.

 

[silverbell]

I got for

3/(8π) ---> 0.119

sin(16π/6) ---> 0.866

cos(16π/6) ---> -0.5

4sin(0) - 4cos(0) ---> 0 - 4

 

[LawrenceC]

Looks like you integrated it properly. I think you evaluated the terms incorrectly.

I suggest you factor the expression as much as possible to remove the 4's. That cleans up your expression and reduces chance of error when cranking through the numbers.

 

[silverbell]

Looks like you integrated it properly. I think you evaluated the terms incorrectly.

I suggest you factor the expression as much as possible to remove the 4's. That cleans up your expression and reduces chance of error when cranking through the numbers.

Thanks for the tip. I got the answers. :D