Multiple Integrals over s square region

Thread starter mit_hacker
Start date Oct 24, 2007
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Integrals Multiple Multiple integrals Square

In summary, a multiple integral over a square region is an integration over a two-dimensional area with two independent variables. It differs from a regular integral, which is a single integral over a one-dimensional interval. The purpose of computing a multiple integral over a square region is to find the total value of a two-dimensional function over a given area, and it can be applied in various fields such as physics, engineering, economics, and statistics. Different methods, including the rectangular, polar, and parametric methods, can be used to evaluate a multiple integral over a square region depending on the function and desired accuracy. It has practical applications, such as calculating work done, total production, and mass or volume of a three-dimensional object.

Oct 24, 2007

mit_hacker

Homework Statement

(Q) Compute ∬_R▒(y-2x^2 )dA where R is a region bounded by the square |x| + |y| = 1.

Homework Equations

The Attempt at a Solution

The absolute functions are throwing me all over the place and I am not even able to begin :cry:

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Oct 24, 2007

EnumaElish

Science Advisor

Homework Helper

How many sub-equations does |x| + |y| = 1 imply? I'll give you one: x + y = 1 if x > 0 and y > 0.

Related to Multiple Integrals over s square region

1. What is a multiple integral over a square region?

A multiple integral over a square region is a type of integral in which the integration takes place over a two-dimensional square area. This means that the function being integrated has two independent variables and the integration is performed over all the points within the square region.

2. How is a multiple integral over a square region different from a regular integral?

A regular integral is a single integral in which the integration is performed over a one-dimensional interval. In contrast, a multiple integral over a square region involves integration over a two-dimensional area, with two independent variables. This means that the result of a multiple integral over a square region is a number, while the result of a regular integral is a function.

3. What is the purpose of computing a multiple integral over a square region?

The purpose of computing a multiple integral over a square region is to find the total value of a two-dimensional function over a given area. This can be useful in various applications, such as calculating the volume under a surface, finding the center of mass of a two-dimensional object, or determining the total charge or mass within a given region.

4. What are the different methods used to evaluate a multiple integral over a square region?

There are several methods that can be used to evaluate a multiple integral over a square region, including the rectangular, polar, and parametric methods. The choice of method depends on the specific function being integrated and the desired level of accuracy.

5. How is a multiple integral over a square region applied in real life?

A multiple integral over a square region has various applications in fields such as physics, engineering, economics, and statistics. For example, in physics, it can be used to calculate the work done by a force over a two-dimensional area, while in economics, it can be used to determine the total production of a company over a given time period. In engineering, it can be used to find the total mass or volume of a three-dimensional object by integrating over a two-dimensional cross-section.