mws_ele_int_txt_trapcontinous_examples - 07.02 Trapezoidal...

07.02.1
07.02
Trapezoidal 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 single segment Trapezoidal rule to find the frequency.
b) Find the true error,
t
E , for part (a).
c) Find the absolute relative true error for part (a).
Solution
a)
 
   







 
2
b f a f
a b I , where
15 . 2   a
9 . 2  b
2