he graph of a function can be symmetric to either the origin or the y-axis. This video demonstrates how the complexity of integrating a function with y-axis symmetry can basically be cut in half. Duration: 7:16

What about origin symmetry? Can such an integral be simplified in the same was as y-axis symmetry? Well, not exactly. I would say that the area bound by that curve doesn't even exist. Duration: 6:04

Will you be able to quickly recognize whether or not you can take advantage of the symmetry rules for integration? The first step is to look to see if your limits of integration are symmetric to the y-axis. Then perhaps you could perform an algebraic test for symmetry. Would that be quicker than just finding the antiderivative? It depends on the integrand in question. Duration: 9:50