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Finding the area of the region between y=x^2+x-12 and the x-axis

For which area am I looking for?

The area below the x axis or above? and why?

Many thanks in advanced

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  • $\begingroup$ The question reads like it was cut off, so I understand why it seems ambiguous. It probably means the area bounded by the curve and the $x$-axis, but this is just a guess. $\endgroup$
    – Hayden
    Commented Mar 19, 2015 at 19:51
  • $\begingroup$ As stated the problem does not make any sense. If I had to guess the problem should read: "Find the area of the region between the line $y=x^2+x-12$ and the $x$-axis." $\endgroup$
    – Eff
    Commented Mar 19, 2015 at 19:51
  • $\begingroup$ Draw a picture. You get an upward-facing parabola that meets the $x$-axis at $x=-4$ and $x=3$. So we want the area of the region below the $x$-axis, but above the parabola. $\endgroup$ Commented Mar 19, 2015 at 19:54

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You are looking for the area below the x-axis (in my graphing program, the gray region).

enter image description here

Consider what would happen if we instead found the area above the axis. It would have no bounds; that is, the area would be infinite.

In general, when integrating, you are looking at the region bounded by the x-axis and the curve. Of course, in some situations (such as those containing vertical asymptotes), you may run in to difficulties.

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