Posted by Anna on .
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