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Application of Integrals

Jammu & Kashmir Board · Class 12 · Mathematics

Complete topic list for Application of Integrals in Jammu & Kashmir Board Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

98 questions60 flashcards5 concepts

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An illustration showing a curve y=f(x) bounded by the x-axis and vertical lines x=a and x=b. The area is approximated by numerous thin vertical rectangular strips, with one representative strip highli
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4 Topics · Jammu & Kashmir Board Class 12 Mathematics

Topics in Application of Integrals

1

1. Core Idea of Area by Integration

  • The elementary area of a thin vertical strip is dA = y dx.
  • Total area under a curve using vertical strips equals the definite integral of f(x).
  • Area bounded by curve x = g(y), y-axis and lines y = c, y = d is found by integrating x with respect to y.
2

2. Negative Area and Mixed Area

  • If the curve lies below the x-axis over [a, b], direct integration gives a negative value.
  • If the computed area is negative, the absolute value is taken as the actual area.
  • If part of the curve is above and part is below the x-axis, the interval must be split.
3

3. Standard Results for Circle and Ellipse

  • The circle x² + y² = a² is symmetrical about both the x-axis and y-axis.
  • Its total enclosed area is found by taking 4 times the area in the first quadrant.
  • The ellipse x²/a² + y²/b² = 1 is also symmetrical about both axes.
4

4. Worked Examples to Remember

  • For the line y = 3x + 2, the x-axis is met at x = -2/3.
  • The area bounded by y = 3x + 2, x-axis, x = -1 and x = 1 is 13/3.
  • The curve y = cos x between x = 0 and x = 2π has total area 4.

Key Concepts

Central concept: Area under curves and bounded regions using definite integrals

Area under a curve with vertical stripsArea under a curve with horizontal stripsArea below the x-axisComposite areaCircle area by integrationEllipse area by integrationWorked example with line and x-axisWorked example with cosine curve

Frequently Asked Questions

What are the important topics in Application of Integrals for Jammu & Kashmir Board Class 12 Mathematics?
Application of Integrals covers several key topics that are frequently asked in Jammu & Kashmir Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Application of Integrals — Jammu & Kashmir Board Class 12 Mathematics?
Understand the core concepts first, then work through the 98 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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