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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.
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.
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The one word you NEVER want to hear from your math teacher.
Teacher: Okay class, here are a few exercises on integrals for you to practice on.
Me: AHHHHHHHHHHHH! *runs out of the classroom*
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some who makes out with somebody while they are drunk or high
You stupid integrator i cant believe you were high when you hooked up with that bitch
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The state of getting your ass handed to you by a acura integra of any year.
dude, your so integrated.
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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
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We need more humans with integrity. Just like Jeremy Corbyn
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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!
Yo u INTEGRATED Beeeaaaaaaaatch!
or..if you want to cuss a male comrade -
Yo u INTERGRATED fellow!
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