Integral calculus is the branch of calculus that deals with integrals and their characteristics. The integral is the reverse function of the derivative. Therefore, the integral is also called anti-derivative. It helps us calculate the area under a curve, the volume, and the solution of a differential equation. This may be challenging to determine without it.
In this article, we will examine the definition of integral with its types. We will learn how to calculate the integration of the given function.
Definition of integral calculus
The integral, denoted by ∫, represents the area under a curve. It consists of two components: Integrand, which is the function being integrated, and the differential, which represents the variable with respect to which the integration is performed.
The integral / anti-derivative is referred to as the inverse process of differentiation. Differentiation calculates a function’s rate of change/slope, while integration allows us to find the original function from its derivative. If g is the differentiable function and g’ express the derivative of g, then the integrating g’ gives the original function g.
Types of Integral
Integral is classified into two types:
- Definite integral
- Indefinite integral
Definite Integral
Definite integral calculates the area under the curves of the function between the specified limits. The definite integral is represented as ∫ab f(x) dx, where ‘a’ is lower and ‘b’ is the upper limit of integration (a < b). A definite integral gives a numeric value, representing the net area between the curve and the x-axis within the specified interval.
Indefinite Integral
The indefinite integral is also known as an antiderivative. This type of integral does not contain specific limits of integration. Integration of f(x) is given by F(x), and it can be written as ∫ f(x) dx = F(x) + C, where C is the constant of integration.