Answer:
At time T the bee will be at (0,0).
The quantity represents the integral of function [tex][r^{'}(u)][/tex] with the time interval of (0,T).
Step-by-step explanation:
Given :
[tex]\int\limits^T_0 {r^{'}(u) } \, du=0[/tex]
As we already know that
[tex]\frac{dr(t)}{dt}=r^{'}(t)[/tex]
Thus we can say that
[tex]\frac{dr(u)}{du}=r^{'}(u)[/tex]
[tex]dr(u)=r^{'}(u)du[/tex]
Now, [tex]\int\limits^0_T {r^{'}(u) } \, du =[r(u)]_{0}^T=r(t)-r(0)[/tex]
[tex]r(t)-r(0)=0\\[/tex]
[tex]r(t)=r(0)=(0,0)[/tex]
So at time T the bee will be at (0,0).
