   Chapter 13, Problem 37RE ### 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 that follows to approximate ∫ 1 2.2 f ( x ) d x using Simpsons Rule. Round your answer to 1 decimal place. X f(x) 1 0 1.3 2.8 1.6 5.1 1.9 4.2 2.2 0.6

To determine

To calculate: The approximate value of 12.2f(x)dx using Simpson's Rule by using the provided table,

 x f(x) 1 0 1.3 2.8 1.6 5.1 1.9 4.2 2.2 0.6
Explanation

Given Information:

The provided integral is,

12.2f(x)dx

And, the provided table for the function is,

 x f(x) 1 0 1.3 2.8 1.6 5.1 1.9 4.2 2.2 0.6

Formula used:

As per the Simpson’s Rule:

If f(x) is continuous on [a,b] and [a,b] is divided into an even number n of equal subdivisions, then,

abf(x)dxh3[f(x0)+4f(x1)+2f(x2)+4f(x3)...+2f(xn2)+4f(xn1)+f(xn)]

Where h=ban.

Calculation:

Consider the provided integral,

12.2f(x)dx

And the provided table for the function is,

 x f(x) 1 0 1.3 2.8 1.6 5.1 1.9 4.2 2.2 0.6

In order to apply the rule, the value of h is as follows:

h=2

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