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.

This is integration defined.

by MIT 2010 January 14, 2007

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.

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.

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

by Atticus Coon March 7, 2005

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.

by FF April 20, 2005

by FuckinFurry January 28, 2019

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!

by Michelle Jane November 13, 2006