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mws_gen_int_spe_trapdiscrete

mws_gen_int_spe_trapdiscrete - Chapter 07.06 Integrating...

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07.06.1 Chapter 07.06 Integrating Discrete Functions After reading this chapter, you should be able to: 1. integrate discrete functions by several methods, 2. derive the formula for trapezoidal rule with unequal segments, and 3. solve examples of finding integrals of discrete functions. What is integration? Integration is the process of measuring the area under a function plotted on a graph. Why would we want to integrate a function? Among the most common examples are finding the velocity of a body from an acceleration function, and displacement of a body from a velocity function. Throughout many engineering fields, there are (what sometimes seems like) countless applications for integral calculus. You can read about a few of these applications in different engineering majors in Chapters 07.00A-07.00G. Sometimes, the function to be integrated is given at discrete data points, and the area under the curve is needed to be approximated. Here, we will discuss the integration of such discrete functions,  b a dx x f I where ) ( x f is called the integrand and is given at discrete value of x , a lower limit of integration b upper limit of integration

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07.06.2 Chapter 07.06 Figure 1 Integration of a function Integrating discrete functions Multiple methods of integrating discrete functions are shown below using an example. Example 1 The upward velocity of a rocket is given as a function of time in Table 1. Table 1 Velocity as a function of time. (s) t ) m/s ( ) ( t v 0 0 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 Determine the distance, , s covered by the rocket from 11 t to 16 t using the velocity data provided and use any applicable numerical technique. Solution Method 1: Average Velocity Method The velocity of the rocket is not provided at 11 t and , 16 t so we will have to use an interval that includes  16 , 11 to find the average velocity of the rocket within that range. In this case, the interval  20 , 10 will suffice. 04 . 227 ) 10 ( v 78 . 362 ) 15 ( v 35 . 517 ) 20 ( v
Integrating Discrete Functions 07.06.3 3 ) 20 ( ) 15 ( ) 10 ( v v v Velocity Average 3 35 . 517 78 . 362 04 . 227 m/s 06 . 369 Figure 1 Velocity vs. time data for the rocket example

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mws_gen_int_spe_trapdiscrete - Chapter 07.06 Integrating...

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