Solving an Integral with a Twist - How to Approach it?

  • Context: Undergrad 
  • Thread starter Thread starter Apteronotus
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary

Discussion Overview

The discussion revolves around the approach to evaluating the integral \(\int f(t) \sqrt{dt}\). Participants explore the validity and meaning of the integral, considering its mathematical formulation and implications.

Discussion Character

  • Debate/contested, Technical explanation

Main Points Raised

  • One participant suggests that the integral is meaningless due to unit inconsistencies.
  • Another proposes a modified version of the integral, \(\int_C f(x,y) \sqrt{dx^2 + dy^2}\), indicating that it could be valid if defined over a contour.
  • Some participants reference a previous discussion on the topic, indicating that context is necessary for further analysis.
  • Another participant argues that the expression \(\sqrt{dx}\) leads to a nonsensical conclusion, implying that the original integral lacks meaning.
  • There is a request for a link to the prior discussion for additional context and insights.

Areas of Agreement / Disagreement

Participants generally disagree on the validity of the integral, with some asserting it is meaningless while others suggest alternative formulations. The discussion remains unresolved.

Contextual Notes

Participants note the importance of context for evaluating the integral, indicating that assumptions about the variables and their definitions are crucial for understanding.

Apteronotus
Messages
201
Reaction score
0
How can the following integral be approached?
[tex] \int f(t) \sqrt{dt}[/tex]

thanks in advance.
 
Physics news on Phys.org
I'm pretty sure it's meaningless. The units don't work out.

However, it would make sense to write something like

[tex]\int_C f(x,y) \sqrt{dx^2 + dy^2}[/tex]

where C is some contour.
 
There was a long argument about this in one of the forums a few months ago. But Apteronotus will have to give us a context before we can say anything about it.
 
It doesn't make sense. Since [tex]\sqrt{x+dx} = \sqrt{x} + \frac{dx}{2\sqrt{x}}[/tex], it follows that [tex]\sqrt{dx} = dx/0[/tex], which is of course meaningless.
 
g_edgar said:
There was a long argument about this in one of the forums a few months ago. But Apteronotus will have to give us a context before we can say anything about it.
Do you have a link to this thread? I'd be interested in reading it.
 

Similar threads

Undergrad How to Approach a Double Exponential Integral?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Another Integration Formula
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Need help with an integral -- How to integrate velocity squared?
  • · Replies 3 ·
Replies
3
Views
2K
High School Integration by parts of inverse sine, a solved exercise, some doubts...
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Non solvable integral? (dx/dt)^2 dt
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Memory issues in numerical integration of oscillatory function
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How do I apply the method of steepest descents to this integral?
  • · Replies 1 ·
Replies
1
Views
3K
High School Integral of cosecant function: understanding different approaches
  • · Replies 14 ·
Replies
14
Views
4K