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

To find the average value of a function over a given interval, you need to perform the following steps:

1. Calculate the definite integral of the function over the interval.
2. Divide the result from step 1 by the length of the interval.

Let's apply these steps to your specific function, f(x) = sin(nx), over the interval from 0 to pi/n.

1. Start by finding the definite integral of f(x) over the given interval. In this case, the integral is:

∫[0, pi/n] sin(nx) dx = [-1/n * cos(nx)] evaluated from 0 to pi/n.

Now we need to substitute the limits of integration into the expression and evaluate it:

= [-1/n * cos(n(pi/n))] - [-1/n * cos(n(0))]
= [-1/n * cos(pi)] - [-1/n * cos(0)]
= [-1/n * (-1)] - [-1/n * 1]
= 1/n - (-1/n)
= 1/n + 1/n
= 2/n

2. Divide the result from step 1 by the length of the interval, which is pi/n - 0 = pi/n:

Average Value = (2/n) / (pi/n)
= 2/n * (n/pi)
= 2/pi

Therefore, the average value of the function f(x) = sin(nx) over the interval from 0 to pi/n is 2/pi.

Based on your explanation, it seems that you have been evaluating the definite integral correctly but haven't divided it by the length of the interval. Make sure to incorporate this step in order to obtain the correct answer.