   Chapter 7.7, Problem 32E

Chapter
Section
Textbook Problem

# (a) A table of values of a function g is given. Use Simpson’s Rule to estimate ∫ 0 1.6 g ( x ) d x . x g(x) 0.0 12.1 0.2 11.6 0.4 11.3 0.6 11.1 0.8 11.7 1.0 12.2 1.2 12.6 1.4 13.0 1.6 13.2 (b) If − 5 ≤ g ( 4 ) ( x ) ≤ 2 for 0 ≤ x ≤ 1.6 , estimate the error involved in the approximation in part (a).

To determine

a) To evaluate: To estimate the value of the integral 01.6f(x) dx by the use of Simpson’s rule, given the values of a function f(x) in the table.

Explanation

Formula used:

Simpson’s rule:

abfxdx=b-a3nfx0+4fx1+2fx2+4fx3..+4fxn-1)+fxn

b-an=h

Calculation:

In the given integral 01.6f(x) dx

b=1.6, a=0, n=8

01

To determine

b) To estimate: The error involved in the approximation in part a)

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