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Find the average value in a calculus approach

  1. Oct 10, 2011 #1
    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. jcsd
  3. Oct 10, 2011 #2

    SammyS

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    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.
     
  4. Oct 10, 2011 #3
    I got for

    3/(8π) ---> 0.119

    sin(16π/6) ---> 0.866

    cos(16π/6) ---> -0.5

    4sin(0) - 4cos(0) ---> 0 - 4
     
  5. Oct 10, 2011 #4
    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.
     
  6. Oct 10, 2011 #5

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