intermediate

Integration — 6-topic bundle

Comprehensive AI-generated study curriculum with 1 detailed note module.

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Course Syllabus

  1. Introduction to Integration and Indefinite Integrals
  2. Techniques of Integration I: Substitution
  3. Techniques of Integration II: Integration by Parts
  4. Definite Integrals and the Fundamental Theorem of Calculus
  5. Applications of Integration I: Area and Volume
  6. Applications of Integration II: Other Applications and Review

Study Notes

Introduction to Integration and Indefinite Integrals

When we differentiated a function, we found its derivative, which tells us the slope of the tangent line at any point or the instantaneous rate of change. Integration is this process backwards. If you have a function that's the derivative of another, integration helps you find that original function.

A function $F(x)$ is an antiderivative of $f(x)$ if the derivative of $F(x)$ is $f(x)$. In other words, if $F'(x) = f(x)$.

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