Pages similar to: Double integrals as volume
- Introduction to double integrals
The definition of a double integral is motivated through a hair density example. - Double integrals as iterated integrals
A description of how to convert double integrals into two single integrals. - Double integral examples
Examples of integrating double integrals over rectangles and triangles. - 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 integrals as area
Explanation of how double integrals could be used to represent area. - 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. - 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. - Area calculation for changing variables in double integrals
A derivation of how a mapping that changes variables in double integrals transforms area. - Double integral change of variable examples
Examples of calculating double integrals through changing variables. - 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. - Length, area, and volume factors
A summary of the expansion factors that arise from mappings in integrals of multivariable calculus. - Volumes by cross sections
Calculating the volume of a solid by integrating the area of its cross sections. - Volume of surfaces of revolution
Calculating the volume of created by rotating a plane region around some axis. - Illustrated example of changing variables in double integrals
An example illustrating with interactive graphics how changing variables transforms regions in the plane. - Volume calculation for changing variables in triple integrals
A derivation of how a mapping that changes variables in triple integrals transforms volume. - Introduction to triple integrals
An introduction to the definition of triple integrals as well as their formulation as iterated integrals. - Triple integral examples
Examples showing how to calculate triple integrals, including setting up the region of integration and changing the order of integration. - Introduction to a line integral of a scalar-valued function
Introduction with interactive graphics illustrating the line integral of a scalar-valued function and informally deriving the formula for calculating the integral from the parametrization of the curve. - Line integrals are independent of parametrization
Description of how the value of a line integral over a curve is independent of the parametrization of the curve. - Examples of scalar line integrals
Examples demonstrating how to calculate line integrals of scalar-valued functions.
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