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Trapezoidal Sum Rule

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This is an example of the Trapezoidal Sum Rule. Here we have the rough average rates of the water exiting the Columbia River at Bonneville Dam on the Oregon and Washington border between 1938 and 1998, where at x=0 is 1938 and every 5 years is marked by 10000x. So at x=120000, the year is 1998. The formula to find the integral of the data, or the sum of the amount of water that flowed out of Bonneville Dam in the 60 year interval, or even simply the sum of the areas of the trapezoids, is the equation:

T = ((b – a)/(2n) )  [ f(x0 ) + 2 f(x1 ) + 2  f(x2 ) + … + 2 f(xn-1 ) + f(xn ) ]

When we use this equation,we find the sum of all the water that flowed from Bonneville Dam from 1938 to 1998 is 1,510,000,000 cubic meters of water. The values for the rate of water flow in the years 1963 and 1998 can be changed to show what would happen to the sum of the water if the flow rate was different for those years.

Tags: Trapezoidal-Rule, Trapezoidal-Sum
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