A definite integral of the form integral [a, b] f(x)dx probably SHOULDN'T be used:

Question

A. (loosely speaking) to calculate "size in four-dimensional space-time" (object's volume multiplied by its duration), by setting f(x)=V(x), letting x represent time, x=a represent the starting time, and x = b the ending time.
B. to calculate power (work/time), by setting f(x)=W(x) (work function), letting x represent time, x=a represent the starting time, and x=b the ending time
C. (loosely speaking) to accumulate infinitely many quantities f(x)dx'' where f(x) represents some physical quantity that s a function of x and dx represents infinitesimal changes in x.
D. to calculate the net change in a quantity whose rate of change with respect to x is given by f(x).

** it may be possible for all answers to be true **

Answer 1

A is weird, but I guess as stated it would make sense.
B is bogus, since the integral would be work * time
C is in fact the very definition of a definite integral
D is ok too (consider integral of velocity = displacement)

Answer 2

So, what would be the best option?

Answer 3

Answer E

Answer 4

B. to calculate power (work/time), by setting f(x)=W(x) (work function), letting x represent time, x=a represent the starting time, and x=b the ending time
is the answer :)