PYQs
Practise questions grouped by chapter and source year.
Practice questions are organised using the years and labels in our source collection. Work through the solutions with your teacher; these are not a complete official examination paper.
Practice question 1
Source year: 20255 marksIntegrate x²+1/(x²-5x+6). [CBSE 2025]
Practice question 2
Source year: 20255 marksEvaluate ∫(x²+1)/(x²-5x+6) dx. [CBSE 2025]
Practice question 3
Source year: 20243 marksFind ∫e²ˣsin(3x) dx. [CBSE 2024]
Practice question 4
Source year: 20223 marksEvaluate the integral: $$ \int x e^x \, dx $$
Solution: Using integration by parts formula $$ \int u \, dv = uv - \int v \, du $$
Let $ u = x $ and $ dv = e^x dx $. Then $ du = dx $ and $ v = e^x $.
$$ \int x e^x \, dx = x e^x - \int e^x \, dx = x e^x - e^x + C = e^x(x - 1) + C $$
Formulae
Revisit important relationships and quick revision formulae.
Integration by Parts
∫udv = uv - ∫vdu
Basic Integrals
∫xⁿ dx = xⁿ⁺¹/(n+1) + C\n∫eˣ dx = eˣ + C\n∫(1/x) dx = ln|x| + C\n∫sin x dx = -cos x + C\n∫cos x dx = sin x + C
Integration by Parts
∫u dv = uv - ∫v du\nILATE rule: I-L-A-T-E priority
Standard Integral Formulas
Source year: 2026- $$ \int x^n \, dx = rac{x^{n+1}}{n+1} + C \quad (n \neq -1) $$
- $$ \int rac{1}{x} \, dx = \log|x| + C $$
- $$ \int e^x \, dx = e^x + C $$
- $$ \int \sin x \, dx = -\cos x + C $$
- $$ \int \cos x \, dx = \sin x + C $$
Notes
Build understanding with chapter guides and revision notes.
Understand the chapter
This is a chapter-wise rendering test file. It is not a full textbook chapter. It contains representative formulae, equations, diagrams, mechanisms, tables, and notation patterns useful for testing digitised CBSE/NCERT-style content.
Metadata
| Field | Value |
|---|---|
| Class | 12 |
| Subject | Mathematics |
| Chapter | 7. Integrals |
| Test type | Markdown + LaTeX + Mermaid |
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Comprehensive Notes: Integrals
Introduction to Integrals
These are the fundamental concepts and key takeaways for this chapter. Make sure to review these before exams.
- Key Concept 1
- Key Concept 2
- Important Definition
More detailed notes will be added here soon.
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