calculus
posted by James .
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)

the average value of the function is
1/(π0) ∫(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
Respond to this Question
Similar Questions

Calculus
Let f be the function given by f(t) = 2ðt + sin(2ðt) a) Find the value of t in the open interval (0,20 for which the line tangent at (t, f(t)) is parallel to the line through (0,0) and (2,4ð) b) Suppose the given function describes … 
calculus
3. Given the function defined by y = x + sinx for all x such that π/2<=x<=3π/2 a. Find the coordinate of all maximum and minimum points on the given interval. Justify your answers. b. Find the coordinates of all points … 
Calculus
I'm supposed to find the average value of the function over the given interval. f(x) = sin(nx), interval from 0 to pi/n, where n is a positive integer. I know the average value formula, and I know that the integral of that function … 
Math
If y = sin−1 x, then sin y = x,−π/2 ≤ y ≤ π/2. Therefore, to find y = sin−1(−3/22, we must find an angle y whose sine is 3/2. There are many possible angles with this sine, but the range … 
Last two CALC questions. :)
8. If f(x) = sin(7 − 5x), find f′(π), which is the derivative at π: −0.754 −0.657 0 * 0.657 3.770 9. Given the function: g(x)={x+b, x<0 {cos(x), x≥0 Find the value of b, if any, that will … 
Trig
Given sin x = 5/13 and 0 < x < pi/2 find the value of sin(π − x). 12/13 5/13 12/13 5/13 
calculus multiple choice
1.The region in the first quadrant bounded by the xaxis, the line x = ln(π), and the curve y = sin(e^x) is rotated about the xaxis. What is the volume of the generated solid? 
Math
We can find the solutions of sin x = 0.6 algebraically. (Round your answers to two decimal places.) (a) First we find the solutions in the interval [0, 2π). We get one such solution by taking sin−1 to get x = ________ (smaller … 
Calculus
Consider the given function and the given interval. f(x) = (x − 3)^2, [2, 5] (a) Find the average value fave of f on the given interval. fave = (b) Find c such that fave = f(c). c = (smaller value) c= (larger value) 
calculus
Consider the given function and the given interval. f(x) = 10 sin(x) − 5 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.)