Class 12 Mathematics — Chapter 8: Application of Integrals
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 12 Mathematics Chapter 8, "Application of Integrals", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 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.
"Application of 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 Application of 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 66.
Key concepts: Application of Integrals (Class 12 Mathematics)
This chapter uses definite integration to find areas under curves and areas bounded between curves and lines.
- Area under a curve
- The area bounded by y = f(x), the x-axis and x = a, x = b is ∫ₐᵇ y dx (taking the magnitude for parts below the axis).
- Area with respect to y-axis
- When integrating along y, the area is ∫_c^d x dy, with x expressed as a function of y.
- Area between two curves
- The area between y = f(x) (upper) and y = g(x) (lower) is ∫ₐᵇ [f(x) − g(x)] dx between their intersection points.
- Handling sign
- Where the curve lies below the axis the integral is negative, so take the absolute value for actual area.
Key formulas — Application of Integrals
💡 Exam tips for Application of Integrals
- Sketch the region first and find the limits from the points of intersection.
- Split the integral where the curve crosses the axis and add absolute values, so areas don't cancel.
Sample questions
Area under y=f(x) from a to b (f≥0):
Definite integral.
Area between y=x and y=x² from 0 to 1:
∫₀¹ (x − x²) dx = 1/2 − 1/3 = 1/6.
Area enclosed by y² = 4x and y = 2x:
Standard exemplar problem.
Application of Integrals — FAQs
What are the key concepts in Class 12 Mathematics Application of Integrals?+
This chapter uses definite integration to find areas under curves and areas bounded between curves and lines. Key ideas include Area under a curve, Area with respect to y-axis, Area between two curves, Handling sign.
What does Class 12 Mathematics Chapter 8 (Application of Integrals) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Application of Integrals" — 22 Easy, 22 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 "Application of Integrals" questions free to practise?+
Yes — sign in with Google to practise "Application of Integrals" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Application of 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.
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