SOLUTION: Electricity is consumed between the hours of midnight (t = 0) and 6 a.m. (t = 6). Selected values of the rate of consumption are shown in the table below, with t measured in hours

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Question 1119906: Electricity is consumed between the hours of midnight (t = 0) and 6 a.m. (t = 6). Selected values of the rate of consumption are shown in the table below, with t measured in hours past midnight, and R(t) measured in KW per hour. Use 4 trapezoids to estimate the total amount of electricity to the nearest KW consumed between midnight and 6 a.m.
t (hours) 0 1 2 5 6
R(t) KW/hr 400 200 350 200 150
Answer by greenestamps(13200) About Me  (Show Source):
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The area of a trapezoid is (height) times (average of the two bases). When used in a problem like this to estimate a total, the height of each trapezoid is the length of the time interval; the two bases are the consumption values at the ends of the time interval.

(1) midnight to 1am: 1 hour; average consumption (400+200)/2 = 300 KW/hr; total consumption 300 KW.
(2) 1am to 2am: 1 hour; average consumption (200+350)/2 = 275 KW/hr; total consumption 275 KW.
(3) 2am to 5am: 3 hours; average consumption (350+200)/2 = 275 KW/hr; total consumption 825 KW.
(4) 5am to 6am: 1 hour; average consumption (200+150)/2 = 175 KW/hr; total 175 KW.

Total estimated power consumption: 300+275+825+175 = 1575 KW.