Can substitution help solve this improper integral?

  • Thread starter Thread starter regnar
  • Start date Start date
  • Tags Tags
    Integrals
Click For Summary

Homework Help Overview

The discussion revolves around evaluating an improper integral involving a logarithmic function and a square root. The integral in question is set from 0 to 1, which raises considerations about convergence and the behavior of the integrand near the lower limit.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to set up the integral and considers the limit as they approach the lower bound. Some participants explore substitution methods, specifically suggesting a transformation involving square roots.

Discussion Status

Participants are actively discussing the substitution method, with some clarifying the nature of the substitution and its implications for the integral. There is an ongoing exploration of the setup and the substitution's relevance, but no consensus has been reached regarding the best approach.

Contextual Notes

The problem involves an improper integral, which introduces complexities related to convergence and the behavior of the integrand at the lower limit of integration. The discussion includes a substitution that may alter the integral's form, but the implications of this transformation are still being examined.

regnar
Messages
24
Reaction score
0
I've been stuck on this problem for quite some time and I get as far as setting up the problem. They are asking me to evaluate this integral:

[tex]\int_0^1{\frac{(6ln4x)}{\sqrt{x}}dx[/tex] and I get as far as:

[tex]\lim_{b \to 0^+}{6\int_b^1{\frac{(ln4x)}{\sqrt{x}}[/tex]
 
Physics news on Phys.org
Substituting x = t^2 seems to work...
 
I'm not sure what you mean or where [tex]t^2[/tex] came from.
 
It's called substitution.

The substitution is [tex]t=\sqrt{x}[/tex] or [tex]t^2 = x[/tex]
 

Similar threads

  • · Replies 105 ·
4
Replies
105
Views
11K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
4
Views
3K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 27 ·
Replies
27
Views
3K
  • · Replies 22 ·
Replies
22
Views
3K