GATE 2022 AG – Question 48
Instrument power (W) at times0,.6,1.2,1.8,2.4,3.0,3.6 s is 8.6,9.2,7.8,6.4,7.2,8.6,11.2. Use Simpson’s1/3 rule to find energy in J, to two decimals.
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Correct answer: 29.20 to 29.50
Explanation
With six equal subintervals h=.6, $E=(h/3)[P_0+P_6+4(P_1+P_3+P_5)+2(P_2+P_4)]$. Thus $E=.2[8.6+11.2+4(9.2+6.4+8.6)+2(7.8+7.2)]=\mathbf{29.32}$ J. Power integrated over time gives energy.