Double Integrals over General Regions, Area, Volume, Mean Value Theorem - Calculus 3

This video explains double integrals over general regions, including the strong form of Fubini's theorem for iterated integrals with variable limits of integration, volume integrals for functions of two variables, properties of double integrals (constant multiple, sum and difference, additive, piecewise over closed bounded planar regions), area of a planar region by double integration, mean value theorem using double integrals to find the average value of a function over a planar region, and worked example practice problems.

0:00 Double integrals over general regions
3:29 Strong form of Fubini's theorem and volume integrals
8:35 Variable limits of integration
16:28 Properties of double integrals
19:35 Area of a planar region using double integrals
20:27 Mean value theorem using double integrals
22:15 Worked examples