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.1. The power or magnitude of light, heat, or whatever else you might analyze in physics class. Intensity is inversely proportional to the square of distance from the source.
2 (a) Excessive and mindless enthusiasm for an activity which is often trivial or pointless. This concept was coined by a group of students from
radnor high school when they were bored during gym class. When you’re playing soccer, Intensity is the voice in your head that tells you to tackle the goalie. Intensity is the Mortal Kombat theme song playing on the nearest boom box when everyone in your gym class has a hockey stick. At the same time, Intensity is getting pumped over something irrelevant. You would be a normal fan if you got insanely pumped for a footbal game, but you would be Intense if you got insanely pumped for a football game between a mediocre team and a really bad team (see Lower Merion High School and radnor). Other legit examples are shouting "defense" as other physics olympics teams try to get their rubber-band powered airplanes off the ground, getting in a fight with another school's mascot, and spirited douche-baggery.
Intensity is generally accepted to be equal to perspiration multiplied by duration. With this meaning, NEVER use the original pronunciation. A good bet is In-tense-it-eye.
2 (b) Getting rowdy
2 (a) Excessive and mindless enthusiasm for an activity which is often trivial or pointless. This concept was coined by a group of students from
radnor high school when they were bored during gym class. When you’re playing soccer, Intensity is the voice in your head that tells you to tackle the goalie. Intensity is the Mortal Kombat theme song playing on the nearest boom box when everyone in your gym class has a hockey stick. At the same time, Intensity is getting pumped over something irrelevant. You would be a normal fan if you got insanely pumped for a footbal game, but you would be Intense if you got insanely pumped for a football game between a mediocre team and a really bad team (see Lower Merion High School and radnor). Other legit examples are shouting "defense" as other physics olympics teams try to get their rubber-band powered airplanes off the ground, getting in a fight with another school's mascot, and spirited douche-baggery.
Intensity is generally accepted to be equal to perspiration multiplied by duration. With this meaning, NEVER use the original pronunciation. A good bet is In-tense-it-eye.
2 (b) Getting rowdy
1. If I differentiate the double integral of the function of intensity... I'll get the first integral... Screw this physics homework, I'm going to go whack off.
2. We totally need to bring the Intensity to the next game. You know, so we'll be Intense.
2. We totally need to bring the Intensity to the next game. You know, so we'll be Intense.
by DJ 'Burth December 11, 2008
Get the Intensity mug.A cell phone with a full keyboard. A decent phone, if only it had more than 20mb of memory and could shoot, send, and recieve VIDEO!
Guy 1: I got the samsung intensity!
Guy 2: Sucks for you, it can't even shoot video!
Guy 1: FFFFFFFFFFFFFF!
Guy 2: Sucks for you, it can't even shoot video!
Guy 1: FFFFFFFFFFFFFF!
by YouMayCallMeV December 1, 2010
Get the samsung intensity mug.by skiracer February 18, 2010
Get the Integrite mug.Intern 1: Man, I feel like I've been here for an internity.
Intern 2: I know right, we'll never get a real job here, might as well start my own business.
Intern 2: I know right, we'll never get a real job here, might as well start my own business.
by Angus704 July 30, 2015
Get the Internity mug.The period of time between graduation and getting an actual paid job. Typically spent in a state of perpetual coffee making and paper filing for little to no reward.
by Escape2Paradox April 10, 2012
Get the Internity mug.by bonquisha April 16, 2004
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