Saturday, June 14, 2025

Evaluating a Double Integral over General Polar Regions of Integration

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  Goal: Evaluate a double integral over a general polar of integration To evaluate the double integral of a continuous function over polar g...
Friday, June 6, 2025

Evaluating a double integral by converting from rectangular coordinates

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  Goal : Evaluate a double integral by converting from rectangular coordinates to polar coordinates  In the last post , we showed how to con...
Monday, June 2, 2025

Double Integrals over a polar rectangular region

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  Goal: Evaluate a double integral over a polar rectangular region Definition The double integral of a function f(r, θ) over a polar rectang...
Tuesday, May 27, 2025

Double Integrals and Expected Values in Probability Theory

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  Expected Values Values In probability theory, we define the expected values E(x) and E(y) as the most likely outcomes of the events. They ...
Friday, May 23, 2025

Applications of double integrals in Probability

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One application of the double integrals over general regions is found in calculating the probability of two random variables. Let's star...
Friday, May 16, 2025

Improper integrals on an unbounded region

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 We previously evaluated a double integral on a bounded region. What if the region is unbounded? The following theorem comes handy for our r...
Tuesday, May 13, 2025

Improper Double Integrals

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  Definition of an improper integral It's preferable to deal with improper integrals of functions over rectangles or simple regions wher...