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Topic review (newest first)
Yes, but it will still have the last edited by... bit so people will know that something's up. Plus, my post is here now.
["Taking an integral is the exact opposite of taking an integral" - you intended to say derivative for one of those, I think. If you want to, just edit your own post and I will delete this comment and it will all look really neat ]
You are getting a little confused with the notation. f(x)=x^2 is the same thing as y=x^2. f'(x) is the same as dy/dx=2x. Taking an integral is the exact opposite of taking an integral. An integral is also called an antiderivative. ∫dy = ∫2x dx is the same as y=x^2.
Thanks, I got it.
But that only works for y=constant?
What I mean is
so the 1/x is like dividing by the class width.
But it doesn't work if it is another function because
and then divide by class width.
But this is different than the following where I divide by first:
And clearly is not the same as
Sorry I left out the dx's in the equations; I don't understand what they are yet. I know it is an incremental piece of x, but I don't know where it is
coming from. Does it appear when you decide to take the integral with
respect to x?
Yes. So, in your example, that would be ∫ (x/10)dx. As I said, they're really just the same thing in a different order.
I don't understand.
Oh you mean divide by 10 and factor out the
before you do the integral?
You can divide by the class width before you integrate instead of afterwards, but that's pretty much the same thing. Other than that, I don't think there's a way.
If you want the average y value (height) of a