Did I Make a Mistake in Computing This Triple Integral?

In summary, the conversation discusses a double integral and whether the computations are correct. The original image was too small and grainy, but a better version was uploaded and deemed correct. However, there was an extra factor of 2 in the calculations that needed to be fixed.
  • #1
-EquinoX-
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  • #2
The image is too small and grainy for me to read clearly...could you upload a larger version of it?
 
  • #3
I uploaded a better image, I hope you can read it now
 
  • #4
-EquinoX- said:
I uploaded a better image, I hope you can read it now

That's much better, and also correct:approve:

(Although it's only a double integral, not a triple integral as the thread title suggests)
 
  • #5
so all my computations there are all correct?
 
  • #6
Edit: no, you have an extra factor of 2...
 
  • #7
where at? the 2pi you mean?
 
  • #8
yes, you brought the 2 inside the integral in order to compute the antiderivative of 2re^(-r^2)dr...but on the next line of your calculation, it was back outside the integral
 

What is a triple integral?

A triple integral is a mathematical concept used in multivariable calculus to calculate the volume under a surface in three-dimensional space. It involves integrating a function over a three-dimensional region.

What is the purpose of computing a triple integral?

The purpose of computing a triple integral is to find the volume of a three-dimensional object or the mass of a three-dimensional object with varying density. It is also used in physics to calculate quantities such as the center of mass and moment of inertia.

What are the different methods for computing a triple integral?

There are several methods for computing a triple integral, including the use of Cartesian, cylindrical, and spherical coordinates. Each method involves a different approach to setting up the integral and may be more suitable for certain types of problems.

What are the limitations of computing a triple integral?

Computing a triple integral can be a complex and time-consuming process, especially for more complicated functions and regions. It also requires a good understanding of multivariable calculus and coordinate systems. In some cases, it may be impossible to find an exact solution and numerical methods must be used instead.

What are some real-life applications of computing a triple integral?

Triple integrals have numerous applications in physics, engineering, and economics. For example, they can be used to calculate the volume of a solid object, the amount of material needed for a construction project, or the total mass of a three-dimensional object with varying density. They are also used in fluid dynamics to calculate the flow of a liquid or gas in a three-dimensional space.

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