What is the generalised integral of the square of a function

Click For Summary
SUMMARY

The discussion centers on the concept of the generalized integral of the square of a function, specifically the integral of f²(x)dx. Participants clarify that there is no universal formula for this integral, as it is highly dependent on the specific function f. The use of u-substitution is mentioned as a technique that may be necessary for evaluating these integrals, particularly for beginners in calculus.

PREREQUISITES
  • Understanding of basic calculus concepts, including integration.
  • Familiarity with u-substitution as a technique for solving integrals.
  • Knowledge of function notation and properties of functions.
  • Basic familiarity with the concept of generalized integrals.
NEXT STEPS
  • Research the application of u-substitution in integral calculus.
  • Study specific examples of integrals involving f²(x) for various functions.
  • Explore the concept of generalized integrals in more depth.
  • Learn about different techniques for evaluating complex integrals.
USEFUL FOR

Students and educators in mathematics, particularly those studying calculus, as well as anyone interested in understanding the complexities of integrating functions.

coverband
Messages
170
Reaction score
1
For example int[f^2(x)dx]
 
Physics news on Phys.org
i think it depends on the function since u have to use u-sub

but not sure, I am a noob :)
 
First, what do YOU mean by "generalized integral"?

If by that you mean simple the integral of f2(x) for general f, as darewinder said, there is no general formula. It depends strongly on what f is.
 

Thread 'How does this derivative work? And why the speed of light remains?'

Relativistic Momentum, Mass, and Energy Momentum and mass (...), the classic equations for conserving momentum and energy are not adequate for the analysis of high-speed collisions. (...) The momentum of a particle moving with velocity ##v## is given by $$p=\cfrac{mv}{\sqrt{1-(v^2/c^2)}}\qquad{R-10}$$ ENERGY In relativistic mechanics, as in classic mechanics, the net force on a particle is equal to the time rate of change of the momentum of the particle. Considering one-dimensional...
View full post »

Similar threads

Undergrad ##L^2## square integrable function Hilbert space
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Another Integration Formula
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Is the functional derivative a function or a functional
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Need help with an integral -- How to integrate velocity squared?
  • · Replies 3 ·
Replies
3
Views
2K
High School Integration by Parts, an introduction I get confused with
  • · Replies 2 ·
Replies
2
Views
2K
High School Integration by parts of inverse sine, a solved exercise, some doubts...
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Integration with different infinitesimal intervals
  • · Replies 31 ·
2
Replies
31
Views
4K
Undergrad Substitution in a definite integral
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Integral -- Beta function, Bessel function?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad What Are Common Misconceptions About the Dirac Delta Function?
  • · Replies 25 ·
Replies
25
Views
4K