Master Integrals – Class 12 Maths Chapter 7 | Indefinite & Definite Integrals, Techniques & CBSE PYQs
Here’s the comprehensive guide for Chapter 7: Integrals from Class 12 CBSE Maths:
🧠 A. Key Concepts & Properties
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Indefinite Integrals
Basic rules:
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, , etc.
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Integration Techniques
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Substitution: Let , then .
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Integration by Parts:
Ideal for polynomial×log/trig.
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Definite Integrals & Fundamental Theorem
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Properties:
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,
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Applications
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Area under curves: (above x-axis)
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Area between curves:
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📘 B. NCERT Exercise-Wise Solutions
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Ex 7.1: Indefinite integrals—apply standard formulas and substitution.
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Ex 7.2: Integration by parts—solve examples like .
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Ex 7.3: Definite integrals—evaluate using FTC; properties problems.
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Ex 7.4: Area between curves—set up integrals and compute area.
Each solution includes:
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Statement
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Step-by-step integration method
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Final result
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Any substitution or limits used
🏆 C. CBSE PYQs with Best Answers
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2023 (5 marks):
Solution: Use part: , . Evaluate and simplify.
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2022 (3 marks):
Find area between curves and from 0 to 1: -
2021 (4 marks):
Solution: Integration by parts with . Answer: .
📌 #Tags:
#Class12Maths, #Integrals, #Calculus, #IntegrationTechniques, #CBSEPYQs, #NCERTSolutions, #AreaUnderCurve, #Chapter7Maths, #BoardExamPrep
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