Given the derivative f’ of the function f, a question that arises is, “Can we determine the function f?” Here, the function f is called antiderivative or integral of f’. The process of finding the antiderivative is called integration. On the other hand, the value of the function found by the process of integration is called an Integral.
For example, the derivative of
f(x) = x3 is f’(x) = 3x2; and the antiderivative of
g(x) = 3x2 is f(x) = x3
Here, the integral of
g(x) = 3x2 is f(x)=x3
Definition of integral: An integral is a function, of which a given function is the derivative. Integration is basically used to find the areas of the two-dimensional region and for computing volumes of three-dimensional objects. Therefore, finding the integral of a function with respect to the x-axis refers to finding the area of the curve with respect to the x-axis. The integral is also called as anti-derivative as it is the reverse process of differentiation.
In general, there are two types of integrals. Definite integrals are defined for integrals with limits and indefinite integrals do not include any limits. Here, let us explore more about definite, and indefinite integrals.