Application of Integrals
CBSE · Class 12 · Mathematics
Quick revision notes for Application of Integrals — CBSE Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Introduction and Basic Concepts
- Elementary geometry formulas are insufficient for calculating areas enclosed by curves
- Integration provides a method to find areas under curves using the limit of sums
- The concept of elementary strips forms the foundation for area calculations
Area Under Simple Curves
- Area under curve y = f(x) between x = a and x = b using vertical strips
- Area bounded by curve x = g(y) between y = c and y = d using horizontal strips
- Total area is the sum of all elementary areas through integration
Handling Negative Areas and Mixed Regions
- When curve lies below x-axis, f(x) < 0 and integral gives negative value
- Physical area is always positive, so take absolute value of negative integrals
- For curves crossing x-axis, split integration at intersection points
Standard Curves and Their Areas
- Areas involving parabolas: y² = 4ax, x² = 4ay
- Areas involving circles: x² + y² = r²
- Areas involving ellipses: x²/a² + y²/b² = 1
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Application of Integrals covers several key topics that are frequently asked in CBSE Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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