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.

Imagine you have a car driving along a road, and its speed changes over time. At some moments, it's going faster; at other moments, it's slower. If you want to find out how far the car travelled over a period of time, you can't just multiply "speed × time" because the speed isn't constant.

Instead, you break the trip into tiny pieces of time (like seconds) where the speed doesn't change much. For each tiny piece of time, you calculate how far the car went at that speed, then add up all those tiny distances.

Key Concepts Related to Integration

This section covers key integration concepts, methods, and applications, including the Fundamental Theorem of Calculus, integration techniques, and how to find areas, volumes, and other geometric properties.

• Introduction to Integration
  • Antiderivative: Integration as Inverse Process of Differentiation
  • Fundamental Theorem of Calculus
• Types of Integrals
  • Definite Integrals
    • Definite Integral as the Limit of a Riemann Sum
    • Properties of Definite Integrals
    • Evaluation of Definite Integrals
  • Indefinite Integrals
  • Improper Integrals
• Riemann Sum
  • Riemann Sums in Summation Notation
• Functions defined by Integrals
• Integration Formulas
• Methods of Integration
  • Integration by Substitution
  • Integration by Trigonometric Subtitution
  • Integration by Parts
  • Integration by Partial Fraction
• Application of Integration
  • Area Under a Curve
  • Area Between Curves
  • Area Between Polar Curves
  • Volume of Solids of Revolution
  • Arc Length of Curves
  • Surface Area of Revolution
• Line Integral
• Surface Integral
• Double Integration
• Triple Integral

Integration Practice

This section provides quizzes and practice questions on integration, covering key topics like basic integration, applications, and integration by substitution.

• Integration - Quiz
• Applications of Integration - Quiz
• Practice Question on Integration by Substitution

Program related to Integration

This section includes programs to help you practice integration and differentiation, such as finding the indefinite integral of a polynomial, differentiating a given polynomial, and calculating double integration.

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