What does the vector ∫b r(t)dt represent?
a
( r(t) is a vector) function)

Question

What does the vector ∫b  r(t)dt  represent?
                                   a
( r(t) is a vector) function)

unklerhaukus · Answer

$$\int\limits_a^br(t)\cdot\text dt$$

anonymous · Answer

i want to know what is that represent, for example, is this a speed of the function, the magnitude/length, or a direction? or something else??

anonymous · Answer

it represents the sum of increments of r in the direction of t

experimentx · Answer

doesn't represent anything is particular .... if r(t) is your force and dt is your displacement  ... then it represents work done.

experimentx · Answer

it represents the total flux of field r(t) passing through the path.

experimentx · Answer

try solving that problem for these two fields
|dw:1347960417651:dw|

experimentx · Answer

|dw:1347960475497:dw|
also try drawing the field along these paths.

unklerhaukus · Answer

r is a function time ,

the integral is the sum of the infinitesimal changes in r from t=a to t=b