# Homework Help: Find the average value in a calculus approach

1. Oct 10, 2011

### silverbell

1. The problem statement, all variables and given/known data

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

Average value: ?

2. Relevant equations

Integrals

3. 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. :)

2. Oct 10, 2011

### SammyS

Staff Emeritus
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.

3. Oct 10, 2011

### silverbell

I got for

3/(8π) ---> 0.119

sin(16π/6) ---> 0.866

cos(16π/6) ---> -0.5

4sin(0) - 4cos(0) ---> 0 - 4

4. Oct 10, 2011

### 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.

5. Oct 10, 2011

### silverbell

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