Chapter 13.8, Problem 2CP

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

True or false:

(a) When the Trapezoidal Rule is used, the number of subdivisions, *n,* must be even.

(b) When Simpsons Rule is used, the number of subdivisions, *n,* must be even.

**(a)**

To determine

Whether the provided statement “When the Trapezoidal rule is used, the number of subdivisions,

Explanation

To develop the Trapezoidal rule formula, it is always assumed that

Within each subdivision, area is approximated using trapezoid.

Thus, since there are no pairs and also, the divisions are

For example, consider the provided integral,

And the value of

And,

For each interval

And,

By using the above formula,

**(b)**

To determine

Whether the provided statement “When the Simpson’s rule is used, the number of subdivisions,

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