March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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Chapter 6
Numerical Integration
In this chapter we will deal with the problem of integration of a function over
an interval,
+
b
a
f(x)dx,
which arises in many situations.
Example 6.1 A manufacturer produces 2-inch wafers. Due to the production
process variability, the actual diameter of wafers made is normally distributed
with a mean of 2 inches and a standard deviation of 0.01 inch. Specifications
require that the diameter is between 1.985 and 2.02 inches. We need to esti-
mate the fraction of the produced wafers that will be acceptable.
Denote by ξ the random variable corresponding to the diameter of a wafer.
We know that ξ has the normal probability density ...
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