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Integrating is the mathematical process used for finding the area under a curve. In principle, this is accomplished by creating a number of rectangles within the area and summing their areas to get an approximation of the total area under the curve. Obviously, the accuracy of the approximation is related to how closely the rectangles fit to the curve. The more rectangles you have, the closer their summed areas matches the area under the curve. At the point where you have an infinite number of rectangles, their summed area exactly matches the area under the curve.
Integration is a mathematical operation performed on the equation of the curve which results in value for the area if the endpoints of the curve are defined (a definite integral) or AA mathematical expression for the area into which endpoints can be plugged (an indefinite integral).
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