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#56 - anonymous poster (12/05/2013) [-]
In basic terms, integrals add up really small shit up. I don't know what physics you're taking but take work as an example. Its change in energy, when you apply a force to something, you change its kinetic energy as long as the force isn't perpendicular to the objects motion. If you think of the force as function, then you need a way of adding up the force at each infinitesimally small increment, integrals do that.
#53 - warrenzthehero (12/05/2013) [-]
Integrals are also called antiderivatives. They're called that for a reason. Basically, they're a derivative in reverse.
In the following examples, I'm going to have small numbers and letters. Those will be powers. I just can't do a superscript in these text boxes. So X2 is X squared, and so on.
The integral of X2 is (1/3)*X3.
To prove it, take the derivative of (1/3)*X3. Using the Power Rule, you get X2.
If you don't know what the Power Rule for Derivatives is, it's
f (x) = Xn
f ' (x) = n * Xn-1
So with our earlier example, the 3 is n and the (1/3) is a scalar, meaning it just sits there and gets multipilied. So you apply the Power Rule, meaning you multiply (1/3) by 3, which gives you 1, and you reduce the power by one, thus giving us X2.
Make sense so far?
For Integrals, it's a little bit more difficult, but not much, so bear with me.
The Power Rule for Integrals is as such
f (x) = Xn
F (x) = (Xn+1) / (n + 1)
So with our example, to integrate X2, you would add one to the power, thus making the numerator X3, and divide by n+1, making the denominator 3.
So we have (X3) / 3, or (1/3)*(X3)
There. I hope I made sense to you. This is just the basics of Integrals and Derivatives, but I can't see you using the really really complex and bran-hurty stuff in Physics. And also I don't know how to do the fancy symbols on here.
Anyway, I hope it helps.
Respond with questions.
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