Difference Between Integration And Differentiation
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Difference Between Integration And Differentiation
Friends in today's session I am going to lay stress on a very important topic of mathematics.
This topic is all about the differentiation and integration and their comparison. These two
topics are the main part of the mathematics.
The differentiation and integration both are used in many fields like physics, engineering etc.
First of al I wil tel you the basic definition of differentiation and integration and then we wil go
for the comparison between them.
Differentiation: The differentiation is a process by which we can find a derivative of any
function.
This is a reverse process of integration. The reverse of the differentiation is also known as anti
differentiation of a function.
It is a very interesting branch of calculus. The derivative of a function can be defined as how
much a quantity changes with respect to the change in another quantity.
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Integration: The Integration is just opposite or reverse process of differentiation; that is also
called anti differentiation.
Now here we are going to discuss the Comparison between Integration and Differentiation:
a. These two terms (named as Differentiation and Integration) are the branch of Calculus that
is one of the very important fields of mathematics. Integration is adding or summing up while
Differentiation is al about dividing.
b. Integration is used to calculate the distance travelled by a function where as the
differentiation is used to calculate the speed of the function.
c. Integration integrates or makes the little fractions to large one and the differentiation divides
a large one into many small fractions.
d. Both are just opposite of each other for example: differentiation d/dx (cos x) =  sin x
Integration cos x = sin x.
e. Differentiation of a given function results in an answer, if we integrate the result or the
answer then we wil again get the function back.
This proves that these both are opposite of each other.
f. The differentiation of a function gives the slope of the function.
For example a linear equation y = mx + c the differentiation of this wil result in m = dy/dx.
Unlike the differentiation the integration gives the area between the given function and its x
axis.
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g. We can say that the differentiation is used to find the change in one quantity with respect to
other quantity where the integration is used to get the area which is covered by the curve of
function with its x axis.
h. Integration is a reverse process of differentiation, for example:
Given function is x = y^3
Differentiating the function with respect to y we get dx/dy = 3y^2
Where the integration of the answer of the differentiation that is 3y^2; we will get
3y^2dy = y^4
Here we can see that by integration of the result of differentiation of a function we again get
the function back.
So this is proved that the integration is a reverse method of differentiation.
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