### Pages similar to: Double integrals as area

- Area calculation for changing variables in double integrals

A derivation of how a mapping that changes variables in double integrals transforms area. - Double integrals as volume

Explanation of how double integrals could be used to represent volume. - Examples of changing the order of integration in double integrals

Examples illustrating how to change the order of integration (or reverse the order of integration) in double integrals. - Double integral change of variable examples

Examples of calculating double integrals through changing variables. - Double integral examples

Examples of integrating double integrals over rectangles and triangles. - Introduction to changing variables in double integrals

Introduction to the concepts behind a change of variables in double integrals. The transformation is illustrated with interactive graphics. - Introduction to double integrals

The definition of a double integral is motivated through a hair density example. - The integrals of multivariable calculus

A summary of the integrals of multivariable calculus, including calculation methods and their relationship to the fundamental theorems of vector calculus. - Area and definite integrals

Integrating to find the area under a curve or the area between two curves. - Double integrals as iterated integrals

A description of how to convert double integrals into two single integrals. - Length, area, and volume factors

A summary of the expansion factors that arise from mappings in integrals of multivariable calculus. - Using Green's theorem to find area

A trick to use Green's theorem to calculate the area of a region - Illustrated example of changing variables in double integrals

An example illustrating with interactive graphics how changing variables transforms regions in the plane. - Double integrals where one integration order is easier

Illustration of a region where integrating a double integral in one order is must easier than integrating in the other order. - Triple integral examples

Examples showing how to calculate triple integrals, including setting up the region of integration and changing the order of integration. - The cross section method for determining triple integral bounds

Explanation of the cross section method for turning a triple integral into a double integral combined with a single integral in order to compute the limits of integration. - The shadow method for determining triple integral bounds

Explanation of the shadow method for turning a triple integral into a double integral combined with a single integral in order to compute the limits of integration. - Calculating the area under a curve using Riemann sums

Approximating the area under the graph of a positive function as sum of the areas of rectangles. - Introduction to triple integrals

An introduction to the definition of triple integrals as well as their formulation as iterated integrals. - Introduction to changing variables in triple integrals

Introduction to the concepts behind a change of variables in triple integrals.