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Application of Integrals — Syllabus

Madhya Pradesh Board · Class 12 · Mathematics

What Application of Integrals covers in Madhya Pradesh Board Class 12 Mathematics: 4 topics, for the 2026-27 session.

98 questions60 flashcards16 formulas & key relations5 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 · Madhya Pradesh Board Class 12 Mathematics · 2026-27

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

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Frequently Asked Questions

What are the important topics in Application of Integrals for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Application of Integrals include Core Idea of Area by Integration, Negative Area and Mixed Area, Standard Results for Circle and Ellipse, Worked Examples to Remember. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How should I revise Application of Integrals for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 98 practice questions on Application of Integrals. Revise 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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All Madhya Pradesh Board Class 12 Mathematics Syllabus

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