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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.