We are already aware of the various method of integration. Let us now have a look on various application of integrals.
One of the major application of integral is in determining the area under the curves.
Consider a function \(y = f(x)\), then the area is given as
\(A = \int_{a}^{b} dA = \int_{a}^{b}y.dx = \int_{a}^{b}f(x)dx\)
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-
\(A = \int_{a}^{b}[f(x) – g(x)]dx\)
