What is Integration in Maths? In Mathematics, integration is the process of adding the parts to find the whole. Integration is the inverse process of differentiation.
We know that, in differentiation, we will find the derivative of the given function, whereas the process of finding the antiderivative of the function is called integration.
Integration serves as a tool to solve complex problems in various fields, especially in Mathematics and Physics. It helps to determine the length of the curve, the area under the curve, the volume of solids, and so on.
In integration, we need to find the primitive function, where the function’s derivative is provided. Integration is one of the major parts of the concept called “Calculus”. The antiderivative of the function is represented by the integral symbol “∫”.
The idea of integration has evolved to solve the two different types of problems. One is to find the primitive function when the derivatives are given. Another is to find the area bounded by the graph function under certain conditions.
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The two types of integrals found in integration process are:
- Definite Integral
- Indefinite Integral
If the integral contains upper and lower limits, then it is called definite integral, whereas if the integrals are not defined with upper and lower bounds, it is called indefinite integral.
The definite integral is also called Riemann integral when the variable of integration is restricted to lie on the real line. As the limits are not defined in an indefinite integral, the result of the integration process should contain a constant value “C” called integration constant.
Another major concept of calculus is differentiation. The derivative of the given function defines the instantaneous rate of change. The concept of differentiation and integration is linked by the fundamental theorem of calculus.
Both the concepts are based on the idea of functions, derivatives, continuity and limits. These are the four key concepts of calculus. A limit is a value that the function approaches some specific value. The limits are used to find the continuity of the function.
The continuity of the function can be easily found using pen and paper. If you trace the graph without lifting the pen from the paper, the function is continuous. If not, the function is discontinuous, as the function’s graph has a gap in between.
In short, differentiation helps to find the rate of change of function, whereas integration helps to find the function when the rate of change is known.
These two concepts play an essential role in the development of modern engineering. Both integral calculus and differential calculus serve as the foundation for higher-level Mathematics. Various rules, like quotient rule, product rule, etc.,
are used to find the function’s derivative. Many concepts like power series, infinite series are developed from the basic calculus concepts like continuity, limits, and so on.
We can say that calculus is the language of mathematics, and often used by statisticians, biologists, economists, etc.
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