IITJEE Advance • Mathematics New Syllabus
Module 09: Integral Calculus Hub
Master the rigorous mathematics of continuous summation and areas. Explore indefinite integrals, advanced reduction formulae, properties of definite integrals, Leibniz rule, and curve area applications.
Topic 1.1 • Anti-Derivatives
Integration as an Inverse Process of Differentiation, Basic Rules, and Standard Formulae
Topic 1.2 • Substitution
Method of Substitution, Trigonometric Substitutions, and Evaluation of Special Integrals
Topic 2.1 • Advanced Methods I
Integration by Parts, ILATE Rule, Classic Forms eˣ[f(x) + f'(x)], and Partial Fractions
Topic 2.2 • Advanced Methods II
Reduction Formulae, Integration of Irrational Algebraic Functions, and Euler Substitutions
Topic 3.1 • Definite Integration
Fundamental Theorem of Calculus, Definite Integral as a Limit of a Sum, and Substitution
Topic 3.2 • Integral Properties
King’s Rule, Even/Odd Functions, Periodic Functions, and Symmetry Properties
Topic 4.1 • Calculus Extensions
Differentiation under Integral Sign (Leibniz Rule), Piecewise Functions, and Integral Inequalities
Topic 4.2 • Area Applications