Chapter 5.4, Problem 70E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Lake Lanier in Georgia, USA, is a reservoir created by Buford Dam on the Chattahoochee River. The table shows the rate of inflow of water, in cubic feet per second, as measured every morning at 7:30 am by the US Army Corps of Engineers. Use the Midpoint Rule to estimate the amount of water that flowed into Lake Lanier from July 18th, 2013, at 7:30 am to July 26th at 7:30 am.

Day | Inflow rate (ft^{3}/s) |

July 18 | 5275 |

July 19 | 6401 |

July 20 | 2554 |

July 21 | 4249 |

July 22 | 3016 |

July 23 | 3821 |

July 24 | 2462 |

July 25 | 2628 |

July 26 | 3003 |

To determine

**To calculate:** The amount of water flowed into the lake from July 18^{th}, 2013 to July 26^{th}, 2013 by using the midpoint rule.

Explanation

**Given information:**

The day July 18 corresponds to time

The day July 26 corresponds to time

The general expression for midpoint rule is shown below:

Apply the conditions for midpoint rule as follows:

Here, width of the subinterval is *b*, the lower limit is *a*, the number of subintervals is *n*, and the midpoint of

**Calculation:**

Find the width of the subinterval

Let us consider the number of subintervals as 4.

Substitute 4 for *n*, 8 days for *b*, and 0 for *a* in Equation (1).

The expression to find the amount of water flowed into the lake using midpoint rule is shown below.

Here, the amount of water flowed into the lake at time

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