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
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by xXINTEGRAXx July 27, 2007
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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.a math class in which everyone wants to be in, but when they are in it would rather not be in it. in other words, it sucks. if you are in integrated math III you know what I mean. integrated math III, it means boring, stupid, hard, annoying, etc.
Evan: Hey, bro, I'm in integrated math three. it is annoying
Coben: really? I wish I was in integrated math three.
Evan: no, you don't.
Coben: really? take me to the classroom then!
Evan: okay if you insist.
coben and evan just walks into straight hell
integrated math III is anoying and stupid
Coben: really? I wish I was in integrated math three.
Evan: no, you don't.
Coben: really? take me to the classroom then!
Evan: okay if you insist.
coben and evan just walks into straight hell
integrated math III is anoying and stupid
by evvannn broooownnn November 11, 2019
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It is the highest form of cussing, refering to DUN DUN DUN.....rock/punk/pop lovers!
It is the highest form of cussing, refering to DUN DUN DUN.....rock/punk/pop lovers!
by PHazz n SophMEISTER December 17, 2003
Get the integrated mug.When you click on a link by accident and then press the back button right after but alas it is too late and you are stuck in between and have a blank page. (Internet Purgatory)
I as searching up why not to play leapfrog with a unicorn when I accidentally clicked on unicorn porn. I pressed back but was stuck in internatory.
by aweRT23 May 23, 2011
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