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 47E

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 : = 0.44444

simpson’s formula:

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

= 0 , = , = ………...=

f(0) = sin(0)c0s(0) = 0

4 f( ) =4(sincos)= 2.2360679774

2 f(2 ) =4(sincos)= 0.363271264

4 f( ) =4(sincos)= 2.236067977

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