Question

f f(x) = sin(x) for all x, then the average value of f on the interval [0, π] is
(A) ½ (B) 1/π (C) π/2 (D) 2/pie

Answer 1

A: When evaluated f(x) = sin(x) on the interval from 0 to pi will give you values that range from 0 to 1. (0+1)/2 = 1/2

Answer 2

Well that's not right.... if you want the average value of a function over an interval, you need to integrate the function over the interval and then divide by the interval's length.

Answer 3

\[average = \int\limits_{0}^{\pi}\sin (x) dx/\int\limits_{0}^{\pi}\ dx\]
use this to get the average
you'll get it to be \[1/\pi\]

Answer 4

\[ 2/\pi..........\]

Answer 5

ya, my fault.