The company tracks its power output Watts every 12 minutes r

The company tracks its power output (Watts) every 12 minutes, resulting in the data below for one day (from 0 power P 1806 1001 2080 336 152 211 410 811 755 630 1350 239 367 1578 21 49 2436 14 28 249 1 384 1 89 8 27 1076 3852 178 2220 162 1091 2067 987 1534 7368 7977 8381 1718 8081 5341 4535 5516 4788 1819 22 2481 2782 2881 1388 2068 2227 626 2249 2780 1206 3346 29:26 1441 1817 1546 3 103 2938 5600 9630 7810 6691 5003 2180 57 1222 67 5996 5640 7526 8970 4352 8323 6174 5202 8639 97 70 9081 1081 5170 1432 5594 4688 7667 8488 9169 9870 5052 1358 504 2540 2929 3815 415 1308 1585 856 1693 2953 2204 1710 1 280 2 260 1 199]; The relationship between energy (Joules) and power (Watts) is that energy is the integral of power with respect to time:

Solution

Matlab Program

P=[1806,1001,2080,336,152,211,410,811,755,630,1350,239,367,1578,2149,1428,2493,1384,1289,827,1076,1230,178,2220,162,1091,2067,987,1534,7368,7977,8381,1718,2328....
8081,5341,4535,5516,7375,4788,1819,4086,3852,8695,2481,2782,2881,1388,2068,2227,626,2249,2780,1706,3346,2926,1441,1817,1546,3103,2938,1722,2776,3781,3137,2823....
438,1560,2364,1838,2020,915,3337,9630,8638,7810,6691,5003,2180,5717,1222,6712,5996,5600,5640,7526,8970,4352,8323,6174,5202,8639,9770,9081,1081,5170,1432,5594....
4688,7667,8488,9169,9870,5052,1358,504,2540,2929,3815,415,1308,1585,856,1693,2953,2204,1710,1280,2260,1199];
t=linspace(12,1440,120)*60;
fun = @(t) P;
E = integral(@(t)fun(t),0,1440,\'ArrayValued\',true);
TotalE=sum(E);

solution is

TotalE =

582354720