Class 12 Maths Chapter 7: Integrals Previous Year Questions
Master Integration through topic-wise previous year questions (2008-2026). These modules cover substitution, integration by parts, partial fractions, and advanced properties of definite integrals.
Choose a method by first recognising the integrand: use standard forms or substitution where appropriate, partial fractions for rational expressions, and the ILATE order to organise integration by parts. The definite-integral sections reinforce symmetry, properties, and absolute-value reasoning for board-level problems.
Topic-wise PYQ Practice
- 1. Standard & Substitution Integrals
- 2. Special Forms & Partial Fractions
- 3. Integration by Parts (ILATE Rule)
- 4. Definite Integrals Properties
- 5. Absolute Value Integrals
Step-wise marking is strictly enforced across all 2-mark, 3-mark, and 5-mark subjective questions. Always quote standard algebraic identities or theorem statements before carrying out algebraic substitutions. For matrix operations and vector cross-products, clearly tabulate intermediate matrix rows and components to guarantee full partial credit even if a minor arithmetic slip occurs in the final step.
CBSE Class 12 Chapter 7: Integrals Blueprint & Exam Strategy
Marks Weightage: Unit III: Calculus (Contributes 8 to 10 Marks, the highest single-chapter weightage). Question blueprint: Includes 2 MCQs (1 Mark each), one 2-Mark or 3-Mark indefinite integral (using substitution, partial fractions, or integration by parts), and one 3-Mark or 5-Mark definite integral evaluated using properties (like King property: integral from 0 to a of f(x)dx = integral from 0 to a of f(a-x)dx).
Examiner Advice: Always write the constant of integration (+ C) for indefinite integrals. In integration by parts (ILATE rule), be careful with negative signs in consecutive integration steps. For definite integrals involving modulus functions |x - c|, split the limits of integration at the critical point c.