Question

What is the opposite of the Integration in Calculus ?

Answer 1

Hint: There are two most important branches of Calculus which are Integral Calculus and Differential Calculus . The Integration comes under Integral Calculus whereas, the Differentiation comes under differential Calculus . Integration is termed as the opposite of differentiation . It is also known as “ antiderivative “ .

Complete step-by-step answer:
Differentiation is considered as the opposite of Integration by the fundamental theorem of Calculus , but it is not exactly the opposite of Integration . The differentiation of a function tells you how the function is changing , whereas the Integral of a function sums up all the values of the function from one point to another point . For better understanding let us take an example
Say we have function \[f(x) = x\] , on differentiating we get \[{f^1}(x) = 1\] but if we want to get back the original function we have to integrate , which results in \[\int {f(x)} \] , on solving we get
\[ = \int x \]
\[ = x + C\] , here \[C\] represents a constant value which is arbitrary .
Therefore , we get our original function back but in addition we also get \[C\] a constant value ( arbitrary ) which is not present initially in the function . So , that is the difference between Integration and Differentiation .
So, the correct answer is “Differentiation”.

Note: The notation \[\int {f(x)} \] without the upper limits and lower limits on the integral sign is used mean “ antiderivative “of the \[\int {f(x)} \] and is known as Indefinite Integral . Integration is used to find the area under the curve by adding a rectangle of length \[d(x)\] for a given equation of the curve .