Application of Integrals for Class 12

Application of Integrals class 12 covers the following concepts:

  • Introduction
  • Areas and Simple curves
  • The area of a region bounded by a curve and a line
  • The area between the two curves

One of the major application of integrals is in determining the area under the curves.

Consider a function \(y = f(x)\), then the area is given as

\(A = \int_{a}^{b} dA = \int_{a}^{b}y.dx = \int_{a}^{b}f(x)dx\)

Application of Integrals Example Problem

Consider the two curves having equation of f(x) and g(x), the area between the region a,b of the two curves is given as-

dA = \([f(x) – g(x)]dx\), and the total area A can be taken as-

\(A = \int_{a}^{b}[f(x) – g(x)]dx\)