Double integrals with absolute function

Thread starter kamikaza007
Start date Sep 5, 2010
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Absolute Function Integrals

In summary, a double integral with absolute function is a mathematical concept used to find the area between a surface and the x-y plane. It involves integrating the absolute value of a function over a region in the x-y plane. To solve it, you must determine the limits of integration for both the x and y variables and use the properties of absolute value to split the integral into two parts. The absolute value function is necessary to accurately calculate the area, and there can only be one unique solution for the integral. This concept is used in real-world applications such as calculating volume and solving optimization problems in physics and engineering.

Sep 5, 2010

kamikaza007

Homework Statement

[PLAIN]http://img704.imageshack.us/img704/453/50838240.jpg

i have trouble with absolute function, can somebody help me how to start

Last edited by a moderator: May 4, 2017

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Sep 5, 2010

hunt_mat

Homework Helper

Ask youself, what is the sign of y-x^{2} in the region you're integrating over? I'll give you a hint, it's of constant sign, what does this mean?

1. What is a double integral with absolute function?

A double integral with absolute function is a mathematical concept used to find the area between a surface and the x-y plane. It involves integrating the absolute value of a function over a region in the x-y plane.

2. How do you solve a double integral with absolute function?

To solve a double integral with absolute function, you must first determine the limits of integration for both the x and y variables. Then, you can use the properties of absolute value to split the integral into two parts and evaluate each separately. Finally, you can add the two results together to get the final answer.

3. What is the purpose of using absolute value in a double integral?

The absolute value function allows us to consider both positive and negative values of a function, which is necessary when finding the area between a surface and the x-y plane. It essentially "flips" negative portions of the function to the positive side, allowing us to accurately calculate the area.

4. Can a double integral with absolute function have multiple solutions?

No, a double integral with absolute function only has one unique solution. This is because the absolute value function is a one-to-one function, meaning that each input has only one output. Therefore, there can only be one possible solution for the area between a surface and the x-y plane.

5. How is a double integral with absolute function used in real-world applications?

Double integrals with absolute function are used in various real-world applications, such as calculating the volume of irregularly shaped objects, finding the center of mass of a 3D object, and determining the work done by a variable force. They are also commonly used in physics and engineering to solve optimization problems.