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.

Question

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

Steve · Accepted Answer

did you draw the graph? The area of a trapezoid is (B+b)/2 * h so, the amount (area) will be (400+200)/2*(1-0) + (200+350)/2*(2-1) + (200+350)/2*(5-2) + (150+200)/2*(6-5) = 1575