   Chapter 13.8, Problem 21E ### 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

# Use the table of values given in each of Problems 19-22 to approximate ∫ b a f ( x )   d x . Use Simpson’s Rule whenever n is even; otherwise, use the Trapezoidal Rule. Round answers to 1 decimal place.Find ∫ 3.6 1.2 f ( x )   d x . X f(x) 1.2 6.1 1.6 4.8 2.0 3.1 2.4 2.0 2.8 2.8 3.2 5.6 3.6 9.7

To determine

To calculate: The approximate value of 1.23.6f(x)dx by Simpson`s Rule if n is even or by Trapezoidal rule if n is odd the table for the values of f(x) shown below.

 x f(x) 1.2 6.1 1.6 4.8 2.0 3.1 2.4 2.0 2.8 2.8 3.2 5.6 3.6 9.7
Explanation

Given information:

The provided function is 1.23.6f(x)dx and the table for the values of f(x) shown below.

 x f(x) 1.2 6.1 1.6 4.8 2.0 3.1 2.4 2.0 2.8 2.8 3.2 5.6 3.6 9.7

Formula used:

The length of each n subdivision for a closed interval [a,b].

h=ban

The approximate value of integral abf(x)dx for n equal subdivision of closed interval [a,b] by Trapezoidal Rule is,

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)++f(xn)]

The approximate value of integral abf(x)dx for n equal subdivision of closed interval [a,b] by Simpson Rule is,

abf(x)dxh3[f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)++f(xn)]

Where h is the length of each subdivision.

Calculation:

Consider the provided integral, 1.23.6f(x)dx

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