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Please help

what does (0-T) represent?

integral from 0 to T

sorry it's the only way I know how to type it

so those are the limits, ok

do you recall the definition of: \[\int_{a}^{b}f(x)~dx=??\]

the fundamental thrm of calculus is also what it is called

It's F(b) - F(a)

for example, cos(pi) - cos(0) = 0 since cos(pi)=cos(0)

but the question is, what does taking the integral of a function tell us?

it can tell you what the area under a curve is

and my example is spose to read cos(2pi) = cos(0), but the site is lagging for me

it's ok

the area under a curve, yes ... but that reflects displacement

ever wonder why in some cases we get a negative area? and in other cases we dont?

Yes because the integral of velocity is displacement

right?

negative displacement ?

displacement on the other hand reflects is a vector, it has magnitude and direction.

Then the location of the bee is still the origin at time T?

yes, at time T, the bee is simply back in the same place it was at when the time was equal to 0

What is the difference between
∫(0-T) r'(u)du = 0
and
∫(0-T) r'(t)dt = 0
Why did they substitute ?

oh ok .. well thank you !

good luck