Integration

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.

• Introduction
• Antiderivative
• Fundamental Theorem of Calculus
• Functions defined by Integrals

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.

• Indefinite Integrals
• Improper Integrals

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.

• Double Integration
• Triple Integral
• Line Integral
• Surface Integral

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.

• Program to find the indefinite Integration of the given Polynomial
• Program to differentiate the given Polynomial
• Program to Calculate Double Integration