integration

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.

by hotgirl69xxx December 22, 2004

Flag

Get the integrationmug.

integrity

Something that certain people in fantasy leagues feel can only be defined by them, AND can only be obtained if you agree with what they say, otherwise you will be called a Fuck Head or a piece of shit.

Cosa feels that because I don't agree with him, I lack integrity.

by F.H.P.O.S. January 8, 2008

Flag