| 2. | integration | ||
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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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| 1. | integration | ||
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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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| 3. | integration | ||
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A mixing of some sort. (Fruit poisoning) <------not good
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| 4. | integration | ||
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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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