IITJEE Mains • Mathematics New Syllabus
Module 08: Integral Calculus Hub
Master the mathematics of accumulation and area. Explore indefinite integrals, advanced integration techniques, definite integral properties, and applications to finding areas.
Topic 1.1 • Anti-Derivatives
Integration as an Inverse Process of Differentiation, Basic Rules, and Standard Formulae
Topic 1.2 • Substitution
Method of Substitution, Integration of Trigonometric Functions, and Special Integrals
Topic 2.1 • By Parts
Integration by Parts, ILATE Rule, and Integrals of the form eˣ[f(x) + f'(x)]
Topic 2.2 • Partial Fractions
Integration of Rational Algebraic Functions using Partial Fractions and Standard Quadratic Forms
Topic 3.1 • Definite Integration
Fundamental Theorem of Calculus, Evaluation of Definite Integrals, and Substitution Limits
Topic 3.2 • Integral Properties
King’s Rule, Even/Odd Functions, Periodic Functions, and Symmetry Properties
Topic 4.1 • Advanced Definite
Differentiation under the Integral Sign (Leibniz Rule), Piecewise Functions, and Inequalities
Topic 4.2 • Area Under Curve