AP CAlc. AB Please helppp!!

Let A(r) be the enclosed by the x axis, the line x=-2, the graph of the function f, and the line x=r for any r=>-2
A) Write A(r) as a piecewise function with its joints at r=0

Please walk me through each step i am really confused!!

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asked by Lily
  1. As usual draw the graph.
    Clearly for r < 0,
    f(x) = -x + 1, so
    A(r) = ∫[-2,r] -x+1 dx

    For r > 0, we have f(x) as
    -x + 1 for -2 <= x <= 0
    x + 1 for 0 < x <= r

    A(x) = ∫[-2,0] -x+1 dx + ∫[0,r] x+1 dx
    Both of those are easy to evaluate, so just plug and chug

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    posted by Steve

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