Ask Question
1 April, 22:04

Consider the given function and the given interval. f (x) = 6 sin (x) - 3 sin (2x), [0, π]

(a) Find the average value fave of f on the given interval.

(b) Find c such that fave = f (c). (Round your answers to three decimal places.)

+5
Answers (1)
  1. 1 April, 22:28
    0
    (a) The average value of the given function is 12/π

    (b) c = 1.238 or 2.808

    Step-by-step explanation:

    The average value of a function on a given interval [a, b] is given as

    f (c) = (1 / (b - a)) ∫f (x) dx;

    from x = b to a

    Now, given the function

    f (x) = 6sin (x) - 3sin (2x), on [0, π]

    The average value of the function is

    1 / (π-0) ∫ (6sinx - 3sin2x) dx

    from x = 0 to π

    = (1/π) [-6cosx + (3/2) cos2x]

    from 0 to π

    = (1/π) [-6cosπ + (3/2) cos 2π - (-6cos0 + (3/2) cos0) ]

    = (1/π) (6 + (3/2) - (-6 + 3/2))

    = (1/π) (12) = 12/π

    f (c) = 12/π

    b) if f_ (ave) = f (c), then

    6sinx - 3sin2x = 12/π

    2sinx - sin2x = 4/π

    But sin2x = 2sinxcosx, so

    2sinx - 2sinxcosx = 4/π

    sinx - sinxcosx = 2/π

    sinx (1 - cosx) = 2/π

    This equation can only be estimated to be x = 1.238 or 2.808
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Consider the given function and the given interval. f (x) = 6 sin (x) - 3 sin (2x), [0, π] (a) Find the average value fave of f on the ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers