# Find the average value of a function

## Homework Statement

Find the average value of a function of f(x)= |x+1| sgnx on the interval [-2,2]

## Homework Equations

The average value formula.

## The Attempt at a Solution

I know I can divide |x+1| into two integrals from [-2,0] and [0,2] (I think?? can anyone confirm this is the proper split?) and add and solve. But what can I do about sgnx?

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Dick
Homework Helper
I would split |x+1| into two intervals. x<(-1) and x>=(-1). And sgn(x) I would split at x=0. You might want to think about splitting |x+1|*sgn(x) into three intervals [-2,-1], [-1,0] and [0,2].

I would split |x+1| into two intervals. x<(-1) and x>=(-1). And sgn(x) I would split at x=0. You might want to think about splitting |x+1|*sgn(x) into three intervals [-2,-1], [-1,0] and [0,2].
Ohh I see why you would split into three pieces. But...if I do split sgn(x) at x=0, which would mean [-2,0] and [0,2] and evaluate with |x| as my integral, wouldn't I get 0? (I know I'm suppose to get 4)

HallsofIvy