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Math Help - Integration of a piece wise function?

  1. #1
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    Integration of a piece wise function?

    Determine the value of:

    a) g(-4)
    b) g(-2)
    c) g(1)
    d) g(4)

    The absolute maximum of g(x) occurs when x=....?

    The absolute maximum of g(x) is...?
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  2. #2
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    Drawing f(x) out would help. You will see that your graph basically consists of line segments.

    Recall that an integral represents the net area under the curve (from the curve to the x-axis). So all you're doing is calculating the areas of the rectangles (taking into account of the signs).

    For example, to find g(1) = \int_{-3}^{1} f(t) \ dt, we want to find the area under the curve from x = -3 to  x = 1

    Since it's a piecewise function, we're going to have to break the integral up into two: g(1) = \int_{-3}^{1} f(t) \ dt = \int_{-3}^{0} f(t) \ dt  + \int_0^1 f(t) \ dt

    If you look at your graph, the two integrals corresponds to the area under each rectangle that is created. I assume you know how to find the area of a rectangle so hopefully you'll be good from here.
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