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 23, 2004
Teacher: Okay class, here are a few exercises on integrals for you to practice on.
Me: AHHHHHHHHHHHH! *runs out of the classroom*
Me: AHHHHHHHHHHHH! *runs out of the classroom*
by Alej0 January 23, 2007
by bonquisha April 16, 2004
dude, your so integrated.
by xXINTEGRAXx June 26, 2007
A very socially desirable trait to have, especially on the internet or in a ghetto. However, the importance of integrity is often way too overemphasized in places such as an elementary school. It would be great if elementary school principles could stop over-preaching the importance of integrity because no kid really gives a shit until around high school. How about upholding some other equally desirable values such as conscientiousness or impartiality.
Literally every elementary/middle school principle during an assembly: I N T E G R I T Y
Me: Integrity deez nuts!!! gOtEm
Me: Integrity deez nuts!!! gOtEm
by Mary Mary Quite The Contrarian September 16, 2021
by Nadsackkkk February 15, 2017
this is the newest word to our beloved hippety hoppety dictionary. Yet use with caution for its intenisity is intensive BLADs!!
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