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 ∫ T 0 r ′ ( u ) d u = 0 ? What does the quantity ∫ T 0 ∥ r ′ ( u ) ∥ d u represent?

At time T the bee will be at (0,0).

The quantity represents the integral of function with the time interval of (0,T).

Step-by-step explanation:

Given :

As we already know that

Thus we can say that

Now,          

So at time T the bee will be at (0,0).

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~