average value of a curve

[perryben]

If I had a sinusoid, how would I find the average value of it over a given interval. Say -pi/5 to pi/5 for instance. Thanks everybody.

[benorin]

The average value of a function, say f(x), over the interval [a,b] is given by the the formula

f_{\mbox{ave}}=\frac{1}{b-a}\int_{x=a}^{b}f(x)dx

where I have assumed that f(x), is properly integrable over [a,b].

[HallsofIvy]

The point is: if you had a constant function, f(x)= c, the "area under the curve" from a to b would f(x)(b-a)= c(b-a). With a variable function, that area is \int_a^b f(x)dx.

If fave is the average of the function we must have
\int_a^b f(x)dx= f_{ave}(b-a)

[mathman]

If I had a sinusoid, how would I find the average value of it over a given interval. Say -pi/5 to pi/5 for instance. Thanks everybody.
The sine function is odd. Therefore the average over an interval symmetric around 0 will be 0.