Let F(x) be a differentiable function of x such that d/dx[F(x)] = f(x). Then F(x) is called as integral of f(x). Symbolically, it is written as ∫f(x) dx = F(x).
f(x), the function to be integrated, is known as integrand.
F(x) is also called as anti-derivative of f(x).
Constant of Integration:
As the differential coefficient of the constant is zero, we know that
Thus, ∫f(x) dx = F(x) + c. This constant c is called as constant of integration and can take any real value instead.
INTEGRATION AS THE INVERSE PROCESS OF DIFFERENTIATION
Anti derivatives of some of extinsively used functions are given below.
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