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The table (supplied by San Diego Gas and Electric) gives the power consumption $ P $ in megawatts in San Diego County from midnight to 6:00 am on a day in December. Use Simpson's Rule to estimate the energy used during that time period. (Use the fact that power is the derivative of energy.)

10,177.3 megawatt-hours

Integration Techniques

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Okay. This question says to estimate the integral of power to find the total energy consumption, and it wants us to use Simpson's rule. So to do this, remember that Simpson's rule says the integral from A to B of f of x d X is approximately equal to the Simpson approximation, which is Delta X over three times Fok, plus for times the odd terms plus two times that even terms plus F a B. So from there, we just need to pick our value. And so there are 13 data points in the table. And remember, R N value is always one less than the total number of puts. So pick an even number and equals 12. So that means that Delta X equals well, we're ending at six, starting at zero, and we want 12 sub intervals. So if 1/2 so that means that s a 12 is equal to 1/2 divided by three, which is 1/6 times off of zero plus four times F of 40.5 plus two times f of one plus four times F 4.5. Plus I just I thought four f 5.5 plus half of six. And then, if you go through and punch all of these function values and your calculator, you'll see that s 12 equals 10 177 megawatt hours, and that's approximately equal to energy.

University of Michigan - Ann Arbor

Integration Techniques