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-

$A = \int_{a}^{b}[f(x) – g(x)]dx$