   Chapter 7.7, Problem 37E

Chapter
Section
Textbook Problem

# 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.) t p 0:00 1814 0:30 1735 1:00 1686 1:30 1646 2:00 1637 2:30 1609 3:00 1604 3:30 1611 4:00 1621 4:30 1666 5:00 1745 5:30 1886 6:00 2052

To determine

To find: The energy used during midnight to 6.00 AM in San Diego County using Simpson’s rule. A table showing power consumption P in Megawatts at various times from midnight is 6.00 AM is given.

Explanation

Formula used:

Simpson’s rule:

abfxdx=b-a3nfx0+4fx1+2fx2+4fx3..+4fxn-1)+fxn

b-an=h

Calculation:

Here b=6, a=0, n=12, so h=1/2

The energy used in San Diego County from midnight to 6 AM is:

E=abPtdt=161814+4×1735+2×1686+4×1646+2×1637+4×1609+2×1604+4×1611+2×1621+4×1666+2×1745+4×1886+2052=10,177

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