Double or triple integral that equals 30

In summary, for the assignment, the person needs to come up with a complex double or triple integral that equals 30. One suggestion is to choose a region in the plane or 3D space (such as a circle or sphere) with an area or volume of 30 and set up the corresponding integral. The integrals should be set up as a function and solved using the fundamental theorem of calculus. This process can also be applied to a single integral by choosing a function and setting it as the integrand, then solving for the corresponding limit. For a double or triple integral, the steps involve picking a function, a region or volume, integrating, and normalizing the result to 30.
  • #1
Mandanesss
37
0
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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  • #2
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?
 
  • #3
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 [tex]f(t)=\int^t_0 x^2 dx[/tex]

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

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

1. How do you solve a double or triple integral that equals 30?

To solve a double or triple integral that equals 30, you will need to integrate the given function over a specific region in two or three dimensions. This can be done by breaking the region into smaller, simpler shapes and using the appropriate integration techniques.

2. What is the difference between a double and triple integral?

A double integral is used to find the volume under a surface in two dimensions, while a triple integral is used to find the volume under a surface in three dimensions. Essentially, a double integral sums up the areas of rectangles, while a triple integral sums up the volumes of rectangular solids.

3. Is there a specific method for solving a double or triple integral that equals 30?

There are various methods for solving double and triple integrals, such as the rectangular, polar, cylindrical, and spherical coordinate systems. The method used will depend on the given function and the region of integration. It is important to understand the properties and limitations of each method.

4. Can a double or triple integral have multiple solutions that equal 30?

No, a double or triple integral will have a unique solution that equals 30. This is because the limits of integration and the function being integrated are fixed, and therefore, the result will be a single, definite value.

5. What is the significance of a double or triple integral equaling 30?

The value of a double or triple integral that equals 30 represents the volume under the given function over a specific region. This can have practical applications in various fields, such as physics, engineering, and economics, where finding the volume of a three-dimensional object or space is required.

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