Double Integral vs Triple Integral
A detailed comparison between Double and Triple integral is given in the table below:
Parameter | Double Integral | Triple Integral |
|---|---|---|
Dimensions | It is an integral of a function of two variables over a two-dimensional region in the xy-plane | It is an integral of a function of three variables over a three-dimensional region in space. |
Region of Integration | Region of integration for a double integral is typically a two-dimensional region bounded by curves or surfaces | Region of integration for a triple integral is typically a three-dimensional region bounded by surfaces |
Application | Double integrals are used to calculate quantities such as area, volume, mass, density, moments of inertia, and probabilities | Triple integrals are used to calculate quantities such as volume, mass, density, moments of inertia, and fluxes over three-dimensional regions |
Integration Order | Double integrals can be evaluated by integrating first with respect to one variable (dx) and then with respect to the other variable (dy), or vice versa | Triple integrals can be evaluated by integrating first with respect to one variable (dx), then with respect to the second variable (dy), and finally with respect to the third variable (dz). |
Also, Check
Double Integral
A double integral is a mathematical tool for computing the integral of a function of two variables across a two-dimensional region on the xy plane. It expands the concept of a single integral by integrating the functions of two variables over regions, surfaces, or areas in the plane. In case two variables are present, we need to substitute the value of one variable in terms of the other. This technique becomes very difficult when we deal with multiple variables to calculate the areas and volumes under the curves. A double integral is very useful in such cases. In this article, we will learn about double integrals in detail.
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