Double or triple integral that equals 30

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Discussion Overview

The discussion revolves around finding complex double or triple integrals that equal 30, focusing on the setup and potential approaches for constructing such integrals. The scope includes mathematical reasoning and exploratory problem-solving related to integrals.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant requests ideas for complex double or triple integrals that equal 30.
  • Another participant suggests using geometric regions, such as a circle or sphere, with areas or volumes that correspond to 30, and setting up the integrals accordingly.
  • A third participant proposes a method involving choosing a function as the integrand, setting limits of integration as variables, and solving to achieve the value of 30, providing an example with a single integral.
  • A fourth participant outlines a general approach: pick a function, select a region or volume, integrate, and normalize the result to 30.

Areas of Agreement / Disagreement

Participants present various methods and ideas for constructing integrals, but there is no consensus on a specific approach or solution. Multiple competing views and strategies remain in the discussion.

Contextual Notes

The discussion does not resolve the specific mathematical steps or assumptions needed to construct the integrals, leaving these aspects open for further exploration.

Mandanesss
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For my assignment I have to come up with a really complex double or triple integral that equals 30.
Would you mind giving me some ideas?
 
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How about picking some region in the plane (a circle perhaps) that has area 30 or a region in 3d (a sphere perhaps) that has volume 30 and set up the corresponding integral?
 
Set up the integrals as a function and solve accordingly, I will start an example for a single integral.

Choose a function, set that as the integrand, set one limit of the integral as another variable, and solve the new function to 30.

eg I choose an integrand x^2.

So I let f(t)=\int^t_0 x^2 dx

Apply the fundamental theorem of calculus we get
f(t) = \frac{t^3}{3}
So now we can let f(t)=30 and solve accordingly.

Do the same but for a double or triple integral.
 
1) Pick a function
2) Pick a region/volume
3) Integrate
4) Normalize to 30
 

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