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07.06.1 Chapter 07.06 Gauss Quadrature Rule for Integration-More Examples Electrical Engineering Example 1: All electrical components, especially off-the-shelf components do not match their nominal value. Variations in materials and manufacturing as well as operating conditions can affect their value. Suppose a circuit is designed such that it requires a specific component value, how confident can we be that the variation in the component value will result in acceptable circuit behavior? To solve this problem a probability density function is needed to be integrated to determine the confidence interval. For an oscillator to have its frequency within 5% of the target of 1 kHz, the likelihood of this happening can then be determined by finding the total area under the normal distribution for the range in question:  dx e x 2 9 . 2 15 . 2 2 2 1 1 a) Use two-point Gauss quadrature rule to find the frequency. b) Find the absolute relative true error. Solution a) First, change the limits of integration from   9 . 2 , 15 . 2 to   1 , 1 using 9 . 2 15 . 2 b a

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