integration
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.
a mixing of some sort.
(fruit poisoning) <------not good
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.
the mixing of blacks and whites during the 30’s and 40’s
integration sucked when elvis was around
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