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

Consider the given function and the given interval.

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 11:50pm
the 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

## Answer This Question

## Related Questions

- Calculus - I'm supposed to find the average value of the function over the given...
- calculus multiple choice - 1.The region in the first quadrant bounded by the x-...
- Calculus - Let f be the function given by f(t) = 2št + sin(2št) a) Find the ...
- Last two CALC questions. :) - 8. If f(x) = sin(7 − 5x), find f′(&#...
- calculus - 3. Given the function defined by y = x + sinx for all x such that -&#...
- calculus - Calculate the left Riemann sum for the given function over the given ...
- Trig - Given sin x = 5/13 and 0 < x < pi/2 find the value of sin(π &#...
- Math - If y = sin−1 x, then sin y = x,−π/2 ≤ y ≤ &#...
- Math - We can find the solutions of sin x = 0.6 algebraically. (Round your ...
- math - Eliminate the parameter (What does that mean?) and write a rectangular ...

More Related Questions