Let f(t), 0≤ t < 24, denote the number of pints drank in the previous hour
Let f(t), 0≤ t < 24, denote the number of pints drank in the previous hour. For example, if between 21.00 and 22.00 you had two pints of beer, then f(t)= 2 when t ϵ (element of) [22, 23). make a plausible graph of f(t). (a) Explain what ʃ(superscript 23)(subscript 0) f(t) dt means. (b) What does the function F(x)= ʃ(superscript x)(subscript 0) f(t) dt represent?
A plausible graph:
Thus no beer from midnight to 8pm; 2 beers each from 8-9 and 9-10pm, 1 beer each from 10-11 and 11pm-12am. (I'm not much of a drinker)
(a) `int_0^(23)f(t)dt` represents the number of pints from 12am to 11pm
(b) `int_0^x f(t)dt` represent the number of pints from 12am to some time x hours later where `0<=x<24`