Skip to main content
Super TutorResources
Chapter 4 of 15
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Revision Notes

Application of Integrals

Madhya Pradesh Board · Class 12 · Mathematics

Quick revision notes for Application of Integrals — Madhya Pradesh Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

98 questions60 flashcards5 concepts

Interactive on Super Tutor

Studying Application of Integrals? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

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
Super Tutor

Super Tutor has 5+ illustrations like this for Application of Integrals alone — flashcards, concept maps, and step-by-step visuals.

See them all

Key Topics to Revise

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.

Get complete notes with diagrams and examples

Full Notes

Key Concepts

A thin vertical strip of heightThe area bounded by the curveThe area bounded by the curveIf a curve lies belowIf part of a curve lies

Frequently Asked Questions

What are the important topics in Application of Integrals for Madhya Pradesh Board Class 12 Mathematics?
Application of Integrals covers several key topics that are frequently asked in Madhya Pradesh 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 — Madhya Pradesh 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.

More resources for Application of Integrals

All 15 chapters — Madhya Pradesh Board Class 12 Mathematics Revision Notes

For serious students

Get the full Application of Integrals chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Madhya Pradesh Board Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free