What is the benefit of differentiation under the integral sign?

  • Context: Undergrad 
  • Thread starter Thread starter Another
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the concept of differentiation under the integral sign, exploring its benefits and applications in mathematical analysis. Participants examine the conditions under which this technique can be applied and its implications for solving integrals that may be otherwise challenging.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • Some participants note that differentiation under the integral sign allows for the interchange of integration and differentiation under certain conditions.
  • Others argue that this technique can simplify the process of finding solutions to integrals that are otherwise complex or impossible to evaluate directly.
  • A participant references external sources, such as Wikipedia, to provide additional context on the topic.

Areas of Agreement / Disagreement

Participants generally agree on the utility of differentiation under the integral sign, but the discussion does not reach a consensus on specific examples or conditions for its application.

Contextual Notes

The discussion does not specify the precise conditions required for differentiation under the integral sign to be valid, nor does it address potential limitations or exceptions to its use.

Another
Messages
104
Reaction score
5
From website https://math.stackexchange.com/questions/43203/integrate-int-fracz-rur2-z2-2rzu3-2-du
28308619_1616503981764221_1883123623_n.png
 

Attachments

  • 28308619_1616503981764221_1883123623_n.png
    28308619_1616503981764221_1883123623_n.png
    10.1 KB · Views: 706
Physics news on Phys.org
QuantumQuest said:
It's differentiation under the integral sign. See Wikipedia here.
What is the benefit of it?
 
Another said:
What is the benefit of it?

Under fairly loose conditions on the function being integrated, differentiation under the integral sign allows one to interchange the order of integration and differentiation. In many cases where the integration is otherwise impossible or is significantly more complex differentiation under the integral sign is able to provide solution.
 

Similar threads

Undergrad Integration Using Trigonometric Substitution
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Gaussian integral by differentiating under the integral sign
  • · Replies 19 ·
Replies
19
Views
5K
MHB Differentiation under integral sign
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Substitution in a definite integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad What would a calculus author have to say on ##\int r^2dm##?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Integration of ##e^{-x^2}## with respect to ##x##
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Differentiating under the integral sign
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad How to integrate with functions of differentials?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
2K