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Area Between Parabolas
Two parabolas are shown, one with a positive quadratic coefficient, the other with a negative quadratic coefficient. Each has the same linear coefficient and between the two parabolas the quadratic coefficient and constant term are transposed. The problem is to determine the area bounded by the intersection of the two parabolas. The result derived gives an area of four-thirds the difference between the constant term and the quadratic coefficient.
The first step to deriving a general result is to establish the points of intersection of the parabolas. These are then used as the limits of integration with the functions to determine the area between the curves.
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