Class 12 Mathematics — Chapter 7: Integrals
68 practice questions · 23 Easy · 23 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 7, "Integrals", with 68 NCERT-aligned multiple-choice questions. The set is split into 23 Easy, 23 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Integrals" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Integrals, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 68.
Key concepts: Integrals (Class 12 Mathematics)
This chapter develops integration as the inverse of differentiation, the main methods of integration, the definite integral, and its key properties.
- Indefinite integral
- ∫f(x)dx is the family of antiderivatives F(x) + C; integration reverses differentiation.
- Methods of integration
- Substitution, integration by parts, partial fractions, and standard formulae handle most integrals.
- Integration by parts
- ∫u·v dx = u∫v dx − ∫[u'·∫v dx] dx; choose u by the ILATE order.
- Definite integral
- ∫ₐᵇ f(x)dx = F(b) − F(a) by the Fundamental Theorem of Calculus; it represents a signed area.
- Properties of definite integrals
- e.g. ∫ₐᵇ f(x)dx = ∫ₐᵇ f(a+b−x)dx, used to simplify symmetric integrals.
Key formulas — Integrals
💡 Exam tips for Integrals
- Use the ILATE rule (Inverse, Log, Algebra, Trig, Exponential) to pick u in integration by parts.
- For definite integrals, the property f(a+b−x) often collapses tough integrals — look for symmetry.
Sample questions
∫ cos x dx =
d/dx (sin x) = cos x, so ∫cos x dx = sin x + C.
∫₀¹ 2x dx =
[x²]₀¹ = 1 − 0 = 1.
∫₋₁¹ x³ dx =
x³ is an odd function. Integral over a symmetric interval [−a, a] is 0.
Integrals — FAQs
What are the key concepts in Class 12 Mathematics Integrals?+
This chapter develops integration as the inverse of differentiation, the main methods of integration, the definite integral, and its key properties. Key ideas include Indefinite integral, Methods of integration, Integration by parts, Definite integral, Properties of definite integrals.
What does Class 12 Mathematics Chapter 7 (Integrals) cover on XamBaaz?+
It covers 68 NCERT-aligned MCQs on "Integrals" — 23 Easy, 23 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.
Are these "Integrals" questions free to practise?+
Yes — sign in with Google to practise "Integrals" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Integrals" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Practise all 68 questions free
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