What is the generalised integral of the square of a function

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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.

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For example int[f^2(x)dx]
 
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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.
 

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