Class 12 NCERT • Mathematics Part 2 (New Syllabus)
Mathematics Part 2 Ch 07: Integrals
Select a topic or study module below to explore integration as inverse differentiation, methods of substitution, trigonometric identities integration, partial fractions, integration by parts, definite integrals, fundamental theorem of calculus, properties, and comprehensive textbook problem solutions.
Topic 01 • Antiderivatives & Formulas
Exploring Indefinite Integrals, Geometric Meaning of Constants of Integration, and Standard Algebraic/Trigonometric Formulas
Topic 02 • Integration by Substitution
Analyzing Change of Variable Methods, Substitution Rule (f(g(x))g'(x) dx), and Standard Results for tan x, cot x, sec x, cosec x
Topic 03 • Trigonometric Integrals
Studying Power-Reducing Formulas, Product-to-Sum Identities, and Special Integrals Involving Sine and Cosine Powers
Topic 04 • Partial Fractions
Investigating Rational Functions, Proper vs Improper Fractions, Non-repeated Linear Factors, and Repeated/Quadratic Factors
Topic 05 • Integration by Parts
Examining ILATE Rule for Product Integration, Integral of e^x(f(x) + f'(x)) dx, and Standard Square Root Formuls
Topic 06 • Definite Integrals & FTC
Analyzing Area under Curves, Limit of a Sum Interpretation, First and Second Fundamental Theorems of Calculus
Topic 07 • Definite Integral Properties
Studying Limit Change during Substitution, Symmetry Properties (Even/Odd Functions), and King Property (Property 4)
Module 08 • Solutions & Chapter Review