Pages similar to: Examples of changing the order of integration in double integrals
- 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 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. - Double integrals as volume
Explanation of how double integrals could be used to represent volume. - Double integrals as area
Explanation of how double integrals could be used to represent area. - 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 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. - Illustrated example of changing variables in double integrals
An example illustrating with interactive graphics how changing variables transforms regions in the plane. - Introduction to triple integrals
An introduction to the definition of triple integrals as well as their formulation as iterated integrals. - 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. - Introduction to a line integral of a vector field
The concepts behind the line integral of a vector field along a curve are illustrated by interactive graphics representing the work done on a magnetic particle. The graphics motivate the formula for the line integral. - Alternate notation for vector line integrals
An alternative notation for the line integral of a vector field is introduced. - Line integrals as circulation
Definition of circulation as the line integral of a vector field around a closed curve. - Vector line integral examples
Example of calculating line integrals of vector fields.