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anonymous
 one year ago
A bee with velocity vector r'(t) starts out at the origin at t=0 and flies around for T seconds. Where is the bee located at time T if ∫(0T) r'(u)du = 0? Also, what does the quantity ∫(0T) r'(u)du represent?
anonymous
 one year ago
A bee with velocity vector r'(t) starts out at the origin at t=0 and flies around for T seconds. Where is the bee located at time T if ∫(0T) r'(u)du = 0? Also, what does the quantity ∫(0T) r'(u)du represent?

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what does (0T) represent?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0integral from 0 to T

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry it's the only way I know how to type it

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1so those are the limits, ok

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1do you recall the definition of: \[\int_{a}^{b}f(x)~dx=??\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1the fundamental thrm of calculus is also what it is called

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1correct, so if F(b)F(a) = 0, then either a=b, or F has the same value at multiple input levels similar to a periodic function.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1for example, cos(pi)  cos(0) = 0 since cos(pi)=cos(0)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1but the question is, what does taking the integral of a function tell us?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it can tell you what the area under a curve is

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1and my example is spose to read cos(2pi) = cos(0), but the site is lagging for me

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1the area under a curve, yes ... but that reflects displacement

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1ever wonder why in some cases we get a negative area? and in other cases we dont?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes because the integral of velocity is displacement

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0negative displacement ?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1when we want to find the area between 2 curves, area is a positive value always ... its an absolute value. And in those cases we have to concern ourselves with the places that one curve crosses over the other.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1displacement on the other hand reflects is a vector, it has magnitude and direction.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1F(b)F(a) = 0 assumes that at a and b, we are in the same place. Either a = b, or we have simply ended were we started.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then the location of the bee is still the origin at time T?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1yes, at time T, the bee is simply back in the same place it was at when the time was equal to 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But why substitute u in for t for the integration? That's the most confusing part. Does that have any effect on the result?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.10 and T are values that the variable u can take on. the function itself is dependant on the value of u ...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the difference between ∫(0T) r'(u)du = 0 and ∫(0T) r'(t)dt = 0 Why did they substitute ?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1hmm, im not absolutely sure, but i think it has something to do with what is called a 'dummy' variable  meant to avoid confusion between the overuse of the letter T

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok .. well thank you !
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