Need help with triple integration problem

Thread starter Nat3
Start date Apr 3, 2011
Tags

Integration Triple integration

In summary, triple integration is a mathematical process used to find the volume of a three-dimensional space. The steps for solving a triple integration problem include determining the limits of integration, setting up the appropriate triple integral, and solving each integral one by one. Some common mistakes to avoid are misinterpreting the limits, integrating with the wrong variable, and forgetting to simplify the final answer. Triple integration is commonly used in physics, engineering, and economics, and there are techniques that can make solving these problems easier, such as using symmetry, a change of variables, or breaking up the integral.

Apr 3, 2011

Nat3

Homework Statement

[tex]\int _0^{\sqrt{\pi }}\int _0^x\int _0^{x z}x^2 \text{Sin}[y]dydzdx[/tex]

Last edited: Apr 3, 2011

Physics news on Phys.org

Apr 3, 2011

Char. Limit

Gold Member

And have you tried anything? I'd start by evaluating that integral wrt y. It should be reasonably straightforward.

Related to Need help with triple integration problem

1. What is triple integration?

Triple integration is a mathematical process used to find the volume of a three-dimensional space by dividing it into infinitely small cubes and adding up the volume of each cube. It is an extension of double integration, which is used to find the area of a two-dimensional shape.

2. What are the steps for solving a triple integration problem?

The steps for solving a triple integration problem are:

Determine the limits of integration for each variable.
Set up the appropriate triple integral based on the given function and limits.
Solve the innermost integral first by integrating with respect to the innermost variable and substituting the limits.
Repeat the process for the remaining integrals, substituting the limits from the previous integral.
Simplify the final answer, if possible.

3. What are some common mistakes to avoid when solving a triple integration problem?

Some common mistakes to avoid when solving a triple integration problem are:

Misinterpreting the limits of integration.
Forgetting to add or subtract the integrals if the limits are not continuous.
Integrating with respect to the wrong variable.
Forgetting to use the correct order of integration.
Not simplifying the final answer.

4. When is triple integration used in real-world applications?

Triple integration is commonly used in physics, engineering, and other scientific fields to calculate volumes, masses, and moments of inertia of three-dimensional objects. It is also used in economics to find the total utility or profit of a product.

5. Are there any techniques to make solving triple integration problems easier?

There are some techniques that can make solving triple integration problems easier, such as:

Using symmetry to simplify the limits of integration.
Using a change of variables to make the integral easier to solve.
Breaking up the integral into smaller parts if the limits are complex.
Using the properties of integrals, such as linearity and the sum rule, to simplify the process.