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 .