Average Value of sin(x)

Calculus 1 · Axiom Academy

EXAMPLE Average Value of sin(x) Use integration to find the average value of a function over an interval Find the average value of on the interval . The average value is the height of a rectangle (orange, dashed) whose area over equals the blue area under the curve. Both regions have area 2 , so the rectangle's height is . Nice work! You found the average value of over straight from the definition. The formula: — total area divided by the width of the interval. Geometric meaning: it is the height of a rectangle on [a,b] with the same area as the region under the curve. The result: for on the average value is . The same definition gives average velocity from a velocity function, average temperature over a day, and many other "typical value" quantities in physics and engineering.

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