simillarities between integration and differentiation

8/2/2019 Simillarities Between Integration and Differentiation

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imillarities

between

Integration andDifferentiation


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Both Differentiation and Integration Distribute overAddition and Subtraction,

d/dx( u v ) = [ d/dx( u ) ] [ d/dx( v ) ]

and

( u v ) dx = ( u dx ) ( v dx ).


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Comparison between

Integration and Differentiation


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These two terms are related to a branch of Basic Mathematics

which is called as Calculus. Integration is Adding up whileDifferentiation is dividing.

Integration tells about the distance travelled by the functionwhile differentiation tells about the speed of the function.

Differentiation makes large distance to very small fractions

while Integration makes the little fractions to large.


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These both are opposite of each other.

Differentiation ofcos issin

Integration ofcos is sin

These are opposites terms of each other.

If we take the differentiation of a function, then take the

integration of the answer, we will complete it with the

function again.

According to the definition, the differentiation of a function is

the slope of a function while the integration is the area

between the function and the x-axis.


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Differentiation finding the rate of change of the

incline/grade of any function

Integration area which is under the curve of

function with respect to the x axis.


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Integration is the reverse of differentiation:

In one way it can be taken as differentiation in reverse.

Lets take a example:

Suppose we will have to differentiate the function

y = x4.

We obtain dy/dx = 4x3.

In Integration we reverse this process and we can say that the

integration of 4x3 is x4.


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In simple way we can say that differentiation is applied

to determine the rates of change of variables and

integration is used to determine lengths, volumes and

areas.


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Let take a example

z = 3x2 +6x

Now means of differentiation is (dy/dx) rate of change of z fora very minute change of x.

We can do differentiation in many steps:

Firstly we multiply the variable 3 by power 2 and power 2 willbe decreased by one. It will be resulted in 6x.

In case of 6x, 6 will be multiplied by power 1 and power 1 willbe decreased by one. It will be resulted in 6

The differentiation of z = 3x2 +6x is dz /dx =6x + 6


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Again suppose:

dy/dx = 6x + 6

Now we are to determine the function from which thisdifferentiation has been derived. The following process

by which we can go back to that function is known as theintegration.

Integration of 6x+6


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We can do integration in many steps:

Firstly we increase the power of variable by one and divide

this variable by increased power.

In case of 6x power of x is given as one. We will increase it by

one that will be 2 and after dividing by 2 it will result in 6x.

In case of 6 the power of x is 0. We will increase it by one that

will be 1 and after dividing by 1 it will result in 3x2.

Then integration of 6x+6 will be as z = 3x2 +6x


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So, in this way we find difference between integration

and differentiation.

simillarities between integration and differentiation

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