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Multivariable calculus, class #19: Changing the order of integration for double integrals
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Mathematician spotlight: Eriko Hironaka
We briefly discuss the mathematical notion of "train tracks." We use a double integral to find the area between a line and a parabola, and write it down in both orders of integration. We use double integrals to compute a probability related to two events (me checking out at the store before you). We do two examples of impossible double integrals that become possible when we change the order of integration, because the particular region we are integrating over gives us the needed "derivative of the inside" that we need in order to find an antiderivative for our function. We draw a region where vertical sections would require two different integrals, but horizontal sections only require one. We recommend to go outside and play in the snow.
We briefly discuss the mathematical notion of "train tracks." We use a double integral to find the area between a line and a parabola, and write it down in both orders of integration. We use double integrals to compute a probability related to two events (me checking out at the store before you). We do two examples of impossible double integrals that become possible when we change the order of integration, because the particular region we are integrating over gives us the needed "derivative of the inside" that we need in order to find an antiderivative for our function. We draw a region where vertical sections would require two different integrals, but horizontal sections only require one. We recommend to go outside and play in the snow.
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