Problem 46E

Using Simpson’s Rule

Approximate the following integrals using Simpson’s Rule Experiment with values of n to ensure that the error is less than 10−3.

Problem 46E

Using Simpson’s Rule

Approximate the following integrals using Simpson’s Rule Experiment with values of n to ensure that the error is less than 10−3.

Answer;

Step 1 of 2 ;

In this problem we need to approximate the integral using simpson’s Rule experiment with values of n to ensure that the error is less than .

Given integral is : dx

The exact value of the given integral is : )=1.959759163 .

simpson’s formula:

Let us consider , f(x) = and n = 10 ,

= 0 , = , = ………...=

f(0) = ln(2+cos(0)) = 1.0986123

f( ) = ln( 2+cos( ) = 1.0821632475 , f( ) = ln( 2+cos( ) =0.52531002

f( ) = ln( 2+cos( ) = 1.328345985 , f( ) = ln( 2+cos( ) =0.34659215

f( ) = ln( 2+cos( ) = 0.95080239495 , f( ) = ln( 2+cos( ) = 0.174779

f( ) = ln( 2+cos( ) =0.83682189 , f( ) = ln( 2+cos( ) =0.227834515

f( ) = ln( 2+cos( )=0.693147175 , f( ) = ln( 2+cos( ) = 1.95975956