Calculus
posted by Anna .
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 would be (1/n)cos(nx), but I keep getting zero for my final answer, which is wrong. Can someone help me?

u = n x
d u = n dx Divide both sides by n
du / n = dx
d x = du / n
integ sin ( n x ) dx =
integ sin u du / n =
( 1 / n ) integ sin u du =
( 1 / n ) (  cos u ) + C =
 cos ( n x ) / n + C
average = [ 1 / ( b  a ) ] definite integral sin( n x ) dx from x = 0 to pi /n
average = [ 1 / ( pi / n  0 ) ] * [  cos ( pi * x / n)  cos ( 0 * x ) ]
average = [ 1 / ( pi / n ) ] * [  cos ( pi * x / n)  1 ]
average = n / pi * [  cos ( pi * x / n )  1 ] 
This answer is wrong people
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
Consider the function f(x)=–3x3–1x2+1x+1Find the average slope of this function on the interval (–2–1). By the Mean Value Theorem, we know there exists a c in the open interval (–2–1) such that f(c) is equal to this mean … 
physics
In this problem you will determine the average velocity of a moving object from the graph of its position as a function of time . A traveling object might move at different speeds and in different directions during an interval of time, … 
Calculus
If b is a positive constant, find the average value of the function f defined by f(x) = x2 + bx + 1 on the interval [1,1] 
calculus
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 … 
Calculus
Find the average value of the function f(x) 8x^29x+8 on the interval [3,5]. Find the value of the xcoordinate at which the function assumes it's average value The average value is ? 
Calculus
Find the average value of the function over [1,3] and all values of x in the interval for which the function: f(x)= 4(x^2+1)/x^2 equals its average value. 
Math
Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = 4x3 − 3x2, [−1, 2] 
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.)