Indefinite integration is the process of finding the antiderivative or the primitive of a function. In other words, it is the reverse process of differentiation. The Class 12 Mathematics syllabus covers the following topics related to indefinite integration:
Integration as the Inverse Process of Differentiation: This topic covers the concept of integration as the inverse process of differentiation and the notation used to represent it.
Standard Integrals: This topic covers the standard integrals of polynomial, trigonometric, exponential, and logarithmic functions.
Integration by Substitution: This topic covers the technique of integration by substitution, also known as the chain rule in reverse.
Integration by Parts: This topic covers the technique of integration by parts, which is used to integrate the product of two functions.
Integration of Rational Functions by Partial Fractions: This topic covers the technique of integrating rational functions by partial fractions.
Integration of Irrational Functions: This topic covers the integration of irrational functions such as algebraic and transcendental functions.
Integration of Trigonometric Functions: This topic covers the integration of trigonometric functions using various trigonometric identities.
Indefinite integration is important because it is a fundamental concept in calculus and is used in various fields such as physics, engineering, economics, and statistics. It provides a powerful tool for calculating areas, volumes, and solving differential equations. The techniques of integration are used in solving problems related to optimization, related rates, and curve sketching. The concepts of integration by substitution, integration by parts, and partial fractions are used in solving complex integrals.