/sci/ - Science & Math » Thread #14234300

11KiB, 222x250, 3g5k6.jpg

View Same Google iqdb SauceNAO

Anonymous Wed 16 Feb 06:11:20 2022 No.14234300 View Reply Original Report

Quoted By:

if the intergrand of a normal integral is the curve which the integral calculates the area under, and the Intergrand of a double integral is the z function for which the volume underneath is sought, what does the integrand of a triple integral represent? what area is it that were looking for? I cant wrap my head around it and its making vector calculus a bitch to learn

Anonymous

Anonymous Wed 16 Feb 2022 06:27:35 No.14234319 Report

Quoted By:

It doesn't need to represent anything, just think its summing over something
perhaps slices of differently shaped volumes or something

Anonymous

Anonymous Wed 16 Feb 2022 06:59:21 No.14234356 Report

Quoted By:

the function doesn't necessarily represent "height". if it does represent height, you can rewrite it as a triple integral whose inner most bounds are your height function. the function you integrate can be any function of however many variables you're integrating.

Anonymous

Anonymous Wed 16 Feb 2022 09:07:16 No.14234573 Report

Quoted By: >>14234725

Don't think of it this way. Think of it as cutting space itself into tiny pieces and taking a sum of the volumes of those pieces weighted by the value of the function. This intuition is unrelated to dimension, just imagine hypercubes instead of cubes.

The area/volume intuition is just to get you started, anyway. General integrals don't necessarily compute volumes.

Anonymous

Anonymous Wed 16 Feb 2022 11:05:36 No.14234725 Report

Quoted By:

>>14234573
This, calculus students should be thought about Riemann sums earlier IMO.

Anonymous

Anonymous Wed 16 Feb 2022 11:14:22 No.14234738 Report

Quoted By:

just as the 3d version of integration is thought of as summing the 2d integrals over a parameter variable, the 4d version sums the 3d integrals over a parameter variable. This can be generalized for any n-dimensional integral

Anonymous

Anonymous Wed 16 Feb 2022 11:24:16 No.14234748 Report

Quoted By:

4 th dimension 4-volume in your logic.

But lets think about
$\int \int \int \rho dxdydz$
you just sum the density function with tiny volume elements.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches