How to Integrate - Understand Integration Factors

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SUMMARY

This discussion focuses on the concepts of integration and integration factors in calculus. Integration is defined as the process of finding an anti-derivative, where one seeks a function F(x) such that F'(x) equals the given function f(x). The term "integration factor" refers to a specific mathematical tool used for solving differential equations, distinct from the general concept of integration. Participants emphasize the need for foundational knowledge before tackling these topics and recommend consulting tutorials or textbooks for deeper understanding.

PREREQUISITES
  • Understanding of basic calculus concepts, including derivatives and anti-derivatives.
  • Familiarity with differential equations and their solutions.
  • Knowledge of mathematical functions and their properties.
  • Access to educational resources such as textbooks or online tutorials on calculus.
NEXT STEPS
  • Study the concept of anti-derivatives in calculus.
  • Learn about integration factors and their application in solving differential equations.
  • Explore online calculus tutorials that cover integration techniques.
  • Review mathematical functions and their derivatives to strengthen foundational knowledge.
USEFUL FOR

Students of mathematics, educators teaching calculus, and anyone seeking to understand integration and its applications in solving differential equations.

yamini
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how to integrate?

can anybody let me know how to integrate?

and

about integration factor?
 
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that's an absurdly large question. you either don't know this, or expect people here to write whole chapters out of textbooks for you
 
kesh said:
...or expect people here to write whole chapters out of textbooks for you

...which they won't do, so you'll browse through the tutorial section or get some instructing material somewhere on the internet, or, consult a book. :wink:
 
radou said:
...which they won't do, so you'll browse through the tutorial section or get some instructing material somewhere on the internet, or, consult a book. :wink:
well i was feeling good humoured enough to check the maths tutorials index before posting my reply. nothing on integration
 
Integration and an integration factor are two very different things. One is your basic anti-derivative, and the other is used for exact differentials.

Integration is easy. Just like addition has its inverse law of subtraction, derivatives have its inverse law of integration. So if you want to find an integral you just figure out what function F(x) would give you the function you are given f(x) when you take its derivative. In other words, find a function F(x) such that F'(x)=f(x).

You are a long way off from integration factors.
 

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