Question

If 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

Here is the formula for finding average function value.
\[\large f_{ave}=\frac{1}{b-a}\int\limits_a^{b}\sin x\;dx\]
So to find the average of our function over the give interval, it will look like this,\[\large f_{ave}=\frac{1}{\pi-0}\int\limits\limits_0^{\pi}\sin x\;dx\]
Do you know how to solve this integral?