quote:

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Originally posted by MattimeoZ80:
integral can be thought of as the anti-derivative...

you can derive and integrate functions. deriving a function generates a function that gives the slope of the initial function at all values x. integrating gives the area under the function, that is the area below the curves to the axis (area below the axis is subtracted or negative). the integral of x^2 is x^3/3. x^3/3 is the area under x^2's curves... not too many curves on x^2 however i'd say something like x(x+1)(x-1)(x+2)(x-2). theres some curves, heh. ah heck, sin(x)'ll do also.

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don't you mean differentiate (or "take the derivative of")? derive means to come up with a formula or proof... My calc teacher gets annoyed if i say "derived" instead of "differentiated."

A derivative more or less just serves as a limiting value when dealing with independant variables.

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WHERE'S THE MOUSEY??
WHERE'S THE MOUSEY??
WHERE'S THE MOUSEY??

n*x^n-1

for example

d/dx (x^2) = 2x

the integral is 1/n+1 * x^n+1

for example

x^2 dx = 1/3 x^3 + C

which is just the reverse of the derivative as you can see. if you were to take the derivative of 1/3 x^3 you would get 3*(1/3)*x^2 = x^2

the C is a constant of integration which is nesscessary because if you take the derivaive of a constant (pi, 1, 2, etc), you get 0. So if an original function had a constant in it, you would not know from the integral. The constant basically represents an offset.

the derivative of a function represents its rate of change. for example, if you had a function which represnted a particle's position as a function of time, the derivative would be a function of the particle's speed. the area under the function is the distance it has traveled (multiply x times dx for all dx = integral of x).

We're doing derivatives and integrals of e-functions in maths now. Funny little things, I must say... quite sweet. e-functions rule.

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LiNeY Croft - Fridge Raider

And, just you wait until you're not talking 1 variable anymore, but you're mixing x's, y's, z's, w's, and t's, plus, you're only considering a few of them at a time, but not others, but they're parametric, blah blah blah. It gets soooo much more painful when you don't follow that y = f(x)

quote:

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Originally posted by LiNeY:
We're doing derivatives and integrals of e-functions in maths now. Funny little things, I must say... quite sweet. e-functions rule.

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e^x dx = e^x
d/dx e^x = e^x

I like e.

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spdfgh

There was once a day where it all made sense.

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WHERE'S THE MOUSEY??
WHERE'S THE MOUSEY??
WHERE'S THE MOUSEY??

And before anyone tries the "you're just too stupid to understand it" card, yes, I have had calc and no, I didn't fail it.

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For birth control, I like to rely on my personality...

Sorry I had to :/

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L'absence est à l'amour ce qu'est au feu le vent; Il éteint le petit, il allume le grand.
- Comte de Bussy- Rabutin