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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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
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Honesty and morality dat's so thorough and complete dat it truly "goes down to da very bottom" of conscientiousness.
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