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Application of Definite Integration

Maharashtra Board · Class 12 · Mathematics & Statistics - Science

Quick revision notes for Application of Definite Integration — Maharashtra Board Class 12 Mathematics & Statistics - Science. Key concepts, formulas, and definitions for last-minute revision.

44 questions20 flashcards5 concepts

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Key Topics to Revise

1

Area Under a Single Curve

  • The definite integral ∫ᵇₐ f(x) dx gives the area under the curve y = f(x) from x = a to x = b
  • If f(x) ≥ 0 in [a,b], then area = ∫ᵇₐ f(x) dx
  • If f(x) ≤ 0 in [a,b], then area = |∫ᵇₐ f(x) dx|
2

Area Between Two Curves

  • Area between curves y = f(x) and y = g(x) is |∫ᵇₐ [f(x) - g(x)] dx|
  • Find intersection points by solving f(x) = g(x)
  • Determine which curve is upper and which is lower in the given interval
3

Special Curves and Their Areas

  • Parabolas: y² = 4ax, area with latus rectum = 32a²/3
  • Circles: x² + y² = r², total area = πr²
  • Ellipses: x²/a² + y²/b² = 1, total area = πab
4

Problem-Solving Strategies

  • Step 1: Identify the curves and region
  • Step 2: Find intersection points
  • Step 3: Determine limits of integration

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Full Notes

Key Concepts

For a continuous curve y =For curves y = f(x)When f(x) ≤ 0 in [aSometimes it's easier to integrateUse symmetry to simplify calculations

Frequently Asked Questions

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Sources & Official References

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

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