Triple Integrals. Need help I cant figure out why 2 integrals arent matching up

In summary, the person is struggling with solving a triple integral in their Calculus 3 class and is seeking help. They have provided an example problem from their book and their own work, but are not getting the same answer as their professor. They suspect the issue may be with the way the theta angle is defined in the problem.
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Triple Integrals
I am currently taking Calc 3 at college and I ran across a small problem with this one triple integral I am trying to work out (The problem is written as Example 1 in the book work document· So far I have had no luck in finding someone who could help me. If you can't help me it's okay, I am just trying to figure out what I am doing wrong. Attached is a copy of the problem from the book and how they did it with the final integration being from 0 to pi/2 and a copy of my work with the final integration being from 0 to pi. According to my professor it should be the same but I am not getting the same answer with this problem or the actual problem I have to do. Any help will be appreciated and if you can't help I understand.

Please try to help if you can...
 

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  • #2


I think the theta angle is defined in a funny way in that excercise. If you have r going from zero to [tex] 2 \sin \theta [/tex], then it goes from zero to zero.
 

1. What is a triple integral?

A triple integral is an extended form of integration that involves integrating a three-dimensional function over a three-dimensional region in space.

2. Why do I have two integrals that aren't matching up?

There could be several reasons for two integrals not matching up. It could be due to a miscalculation, an error in setup, or the integrals representing different regions or functions.

3. How do I solve a triple integral?

To solve a triple integral, you first need to set up the integral by identifying the limits of integration for each variable. Then, you can evaluate the integral using various techniques such as Fubini's theorem, substitution, or integration by parts.

4. What is the purpose of using triple integrals?

Triple integrals are used to calculate the volume, mass, and other physical quantities of three-dimensional objects or regions. They are also used in various fields of science, such as physics, engineering, and economics, to solve complex problems involving three variables.

5. Can I use a calculator to solve a triple integral?

Yes, there are several online calculators and software programs that can help you solve triple integrals. However, it is important to understand the concepts and techniques behind solving them to ensure accurate results.

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