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The integral gives the area under the curve.
If it's an even function, the graph for negative x will be a reflection in the y axis of the graph for positive x.
It follows that the area under the curve, and thus the integral, between a and -a will be double that between 0 and a (or indeed, -a and 0).
If it's an even function, the graph for negative x will be a reflection in the y axis of the graph for positive x.
It follows that the area under the curve, and thus the integral, between a and -a will be double that between 0 and a (or indeed, -a and 0).
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