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Application of Integrals

NCERT Class 12 Mathematics Chapter 8

Application of Integrals for Class 12 Maths and JEE: area under simple curves, areas of circles and ellipses, and the area between two curves.

2 topics Updated 7 Nov 2026

For: Class 12 and JEE, unless a topic says otherwise

In the syllabus: JEE Class 12 syllabus

With your textbook

NCERT Mathematics Part II (Class 12), Chapter 8 “Application of Integrals”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.4 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Area under simple curves

    Area under the curve for Class 12 Maths and JEE: vertical and horizontal strips, parts below the x-axis, circle and ellipse areas, solved NCERT questions.

    NCERT Section 8.2 12 min read 5 solved examples 10 practice questions

  2. Area between two curves

    Area between two curves for JEE Main: top minus bottom, limits from intersection points, horizontal strips, solved parabola, line and circle examples.

    JEE only 12 min read 5 solved examples 11 practice questions

Key formulas in this chapter

Area under curves

  • A = ∫ |y| dx from x = a to x = b, a < b
  • A = ∫ |x| dy from y = c to y = d, c < d
  • circle x + y = a: area πa
  • ellipse x/a + y/b = 1: area πab

Area between curves

  • A = ∫ [f(x) − g(x)] dx from x = a to x = b, f on top
  • A = ∫ [p(y) − q(y)] dy from y = c to y = d, p on the right
  • limits: solve f(x) = g(x)

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