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 15, 2007
Get the integration mug.by Atticus Coon May 13, 2005
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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.
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
Get the integration mug.When during integration that doesn't go smoothly (they rarely do) an engineer start questioning the life choices that got him into this mess.
co-worker: how is integration going?
engineer: I should have went to arts school. If only I wasn't so dependent on my fathers approval
co-worker: so... the usual integration hell?
engineer: I think the only way to fix this bug is to leave my wife, foreclose on the mortgage and move to maine to open a small bakery
engineer: I should have went to arts school. If only I wasn't so dependent on my fathers approval
co-worker: so... the usual integration hell?
engineer: I think the only way to fix this bug is to leave my wife, foreclose on the mortgage and move to maine to open a small bakery
by pizzamaster June 1, 2021
Get the Integration Hell mug.Arguably one of the more challenging concepts to learn in integral calculus, integration by parts is the process by which you find the integral of 2 expressions multiplied together. The most common formula for doing this is "udv = uv -integral(vdu)," but an easier way to view it is "uv = (u * integral(v)) - (integral(u' - integral(v))"
Integration by parts is a very tricky concept to learn at first, but with some time and practice can become easier to do and often amusing for calculus students.
by University of Markov December 30, 2020
Get the Integration by Parts mug.A term used by programmers when they try to make several mechanics that work on themselves work with each other the attempt at fixing this mess is called integration hell because strying to fix a part of the program without messing up other parts of the program is really hard
ex: trying to make the program work without making it unneccesarily long or very laggy is integration hell.
- a person who dosent know much about programming.
- a person who dosent know much about programming.
by anonymous December 13, 2022
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