   Chapter 13.8, Problem 2CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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, n, must be even.”

Explanation

To develop the Trapezoidal rule formula, it is always assumed that f(x)0 on [a,b] and then subdivide the interval [a,b] into n equal pieces, each of length ban.

Within each subdivision, area is approximated using trapezoid.

Thus, since there are no pairs and also, the divisions are n equal pieces, so the number of divisions can be both even and odd.

For example, consider the provided integral,

014dxx2+1dx

And the value of n is 5 which is odd.

And,

a=0, b=1

For each interval [a,b] and value of n,

h=ban

And,

xn=a+nh

By using the above formula,

h=105=15

 i xi=a+ih f(xi)=4x2+1 0 0 4 1 0

(b)

To determine

Whether the provided statement “When the Simpson’s rule is used, the number of subdivisions, n, must be even.”

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