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Don't listen to the guy above talking about integration. Integration is NOT the reversal of differentiation. That would be the anti-derivative. Integrals and anti-derivatives are NOT the same thing. But they are connected by the Fundamental Theorem of Calculus.
If a function f(x) has an anti-derivative F(x), the area under the curve from a to b is equal to F(b)-F(a).
This is integration defined.
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the mixing of blacks and whites during the 30's and 40's
Integration sucked when Elvis was around
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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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Doing the right thing even when nobody's looking.
Jimmy showed his integrity by not looking at the answers to the test when every other cheating bastard in his class was passing them out.
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Adherence to moral and ethical principles; soundness of moral character; honesty.
Having integrity is not lying - in otherwords, doing what you said you would do. OPPOSITE OF INTEGRITY: Telling her you are going to call, and then NOT calling. That's the definition of a Scumbag!
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Note:This definition of integral is alternate to the mathematical type of integral.
Something that, by attempting to do its intended task, inadvertently does the opposite.
Despite popular belief, this does not include things that are broken, such as something that doesn't work or is used improperly.
A: I thought of an Integral! There were so many garbage cans on the beach it actually made the beach look less clean.
B: Nice one!
A: I thought of an Integral! I wanted to have fun so I started drinking, but then I drank too much and I threw up and no longer had fun.
B: That's not an integral! You're just stupid.
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