A chemical reactor releases heat at a rate H(t) measured in kilojoules per minute, where t is the number of minutes after the beginning of a monitoring period. Measurements of the heat–release rate are recorded in the table below.
t (min)
0
4
8
12
16
H(t) (kJ/min)
520
480
450
430
415
(a) Interpret the definite integral ∫016H(t)dt in the context of this situation, including appropriate units.
(b) A technician estimates the total heat released during the 16-minute period by multiplying the first recorded rate by the entire 16-minute time interval. Explain whether this estimate is an overestimate or an underestimate of ∫016H(t)dt, using evidence from the data.
(c) The technician then proposes using the last recorded rate instead. Without performing any numerical calculations, explain how and why the direction of the error would change if the last recorded rate were used for the entire interval.