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December 21, 2014

December 21, 2014

Posted by **James** on Monday, February 11, 2013 at 11:24pm.

f(x) = 4 sin x − 2 sin 2x, [0, π]

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

fave =

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

c = (smaller value)

c = (larger value)

- calculus -
**Reiny**, Monday, February 11, 2013 at 11:50pmthe average value of the function is

1/(π-0) ∫(4sinx - 2sin 2x)dx from x = 0 to π

= (1/π) [-4cosx + cos 2x] from 0 to π

= (1/π) ( -4cosπ + cos 2π - (-4cos0 + cos0) )

= (1/π)( 4 + 1 - (-4 + 1) )

= (1/π)(8) = 8/π

b) if 4sinx - 2sin 2x = 8/π

2sinx - sin 2x = 4/π

2sinx - 2sinxcosx = 4/π

sinx - sinxcosx = 2/π

nasty equation to solve, I ran it through Wolfram to get

x or c = 1.238224 or c = 2.80812

http://www.wolframalpha.com/input/?i=sinx+-+sinxcosx+%3D+2%2Fπ

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