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Negative area between two curves

  1. Dec 9, 2013 #1
    I've been trying to figure out what a negative area means, but I can't.

    The problem statement, all variables and given/known data
    Calculate the area between [itex]f(x) = 3^{x} \, , \, g(x)=2x+1[/itex]

    The attempt to a solution
    The intersections are located in [itex]x=0[/itex] and [itex]x=1[/itex].
    So I do the integral from 0 to 1.
    [itex]\int_{0}^{1} (g(x)-f(x))dx = \frac{2}{log(3)}-2 \approx -0.17952154675[/itex]

    What am I doing wrong? I am integrating the upper function minus the lower function.
  2. jcsd
  3. Dec 9, 2013 #2


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    Gold Member

    The Negative is only telling that the function [itex]3^x-2x-1 [/itex],has negative values more than positive ones inside the interval of integration and of course by integrating [itex]2x+1-3^x [/itex] you will get a positive answer!It is obvious from this that the sign doesn't mean much.
  4. Dec 9, 2013 #3
    No, you have swapped f(x) and g(x) in this step.
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