Integration, in simple terms, is a way to add up small pieces to find the total of something, especially when those pieces are changing or not uniform.
- It is often called the reverse of differentiation.
- Process of finding an integral, which represents the accumulation of small quantities over an interval.
Integration is used to find
- Areas under curves
- Volumes of solids
- Distance from velocity
- Total growth or accumulation
- Probability in statistics
Basics
Learn the core concepts of integration, including antiderivatives, the Fundamental Theorem of Calculus, and integral functions.
Riemann Sums & Definite Integrals
Understand how integration arises from sums and how definite integrals are evaluated.
- Riemann Sum
- Riemann Sums in Summation Notation
- Definite Integral as the Limit of a Riemann Sum
- Definite Integrals
- Properties of Definite Integrals
- Evaluation of Definite Integrals
Types of Integrals
Explore different types of integrals and their uses in solving accumulation problems.
Methods of Integration
Learn essential formulas and techniques for evaluating integrals efficiently.
- Integration Formulas
- Methods of Integration
- Integration by Substitution
- Integration by Trigonometric Subtitution
- Integration by Parts
- Integration by Partial Fraction
Applications
Discover how integration is used to find areas, volumes, and other geometric quantities.
- Application of Integration (Overview)
- Area Under a Curve
- Area Between Curves
- Area Between Polar Curves
- Volume of Solids of Revolution
- Arc Length of Curves
- Surface Area of Revolution
Multivariable & Advanced Integration
Extend integration to multiple variables and vector fields for higher-dimensional problems.
Practice
Test your understanding with quizzes and practice problems on integration..
- Integration - Quiz
- Applications of Integration - Quiz
- Practice Question on Integration by Substitution
For Programmers
Practice integration concepts through programming-based implementations and calculations.