For the function f(x)= cases x, & 0 x 1, 2-x, & 1<x 2

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

For the function

f(x)=\begin{cases}x, & 0\le x\le 1,\\2-x, & 1<x\le 2,\end{cases}

state the two sub-intervals over which you must integrate separately when finding its average value on

[0,2]

, and briefly explain why the split is necessary.