Finding the Area Between the Axes and a Curve That Crosses the Axes

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The graph above shows the curveTo find the shaded area it is not enough to integrate betweenandThe area betweenandwhich is below the axis, will make the whole answer negative. Since the area is always positive our approach to the question will be this:

Split the area into two areas.will be that part of the graph for whichand will be that part of the graph for whichFor each area we apply the formula

Forthe top will be the curveand the bottom will be the– axis, and forthese will swap over.

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