by beingnoob February 25, 2010
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the reverse process of differentiaton
we know that, for example if f(x) = 2x^3 - 5x^2 + 3x -7
then f'(x) = 6x^2 - 10x + 3
This process can be reversed.
In general, y = x^n -> dy/dx = nx^(n-1)
So, reversing this process, it would seem that dy/dx = x^m -> y = (1/(m+1))x^(m+1)
The general process of finding a function from its derivative is known as interation.
we know that, for example if f(x) = 2x^3 - 5x^2 + 3x -7
then f'(x) = 6x^2 - 10x + 3
This process can be reversed.
In general, y = x^n -> dy/dx = nx^(n-1)
So, reversing this process, it would seem that dy/dx = x^m -> y = (1/(m+1))x^(m+1)
The general process of finding a function from its derivative is known as interation.
Given that dy/dx = 12x^2 + 4x - 5, find an expression for y.
y = 12((x^3)/3) + 4((x^2)/2) - 5((x^1)/1)
It would seem that
y=4x^3 + 2x^2 - 5x
but that is not quite the complete answer
Whenever you differentiate a constant you get zero,
e.g. y = 7 dy/dx = 0
and so the expression for y above could have any constant on the end and still satisfy dy/dx = 12x^2 + 4x - 5
The answer to this example is therefore
y= 4x^3 + 2x^2 - 5x + c, where c is a constant.
y = 12((x^3)/3) + 4((x^2)/2) - 5((x^1)/1)
It would seem that
y=4x^3 + 2x^2 - 5x
but that is not quite the complete answer
Whenever you differentiate a constant you get zero,
e.g. y = 7 dy/dx = 0
and so the expression for y above could have any constant on the end and still satisfy dy/dx = 12x^2 + 4x - 5
The answer to this example is therefore
y= 4x^3 + 2x^2 - 5x + c, where c is a constant.
by hotgirl69xxx December 22, 2004
Get the integration mug.Intergrating e^ax+b = (e^ax+b)/a +c
by Atrus Machina May 18, 2005
Get the intergration mug.A term used by programmers when they try to make several mechanics that work on themselves work with each other the attempt at fixing this mess is called integration hell because strying to fix a part of the program without messing up other parts of the program is really hard
ex: trying to make the program work without making it unneccesarily long or very laggy is integration hell.
- a person who dosent know much about programming.
- a person who dosent know much about programming.
by anonymous December 13, 2022
Get the Integration hell mug.by Awesome8080 April 28, 2009
Get the Sexual Trilateral Integration mug.Rational interaction; UML 2 interaction overview diagrams are variants on UML activity diagrams which overview control flow
Interation of Forinform, Forinformation and Forminform results in Virtualculture.
by Hercolena Oliver July 10, 2010
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