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Solution: Using Simpson’s Rule Approximate the following
Chapter 5, Problem 47E(choose chapter or problem)
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 \(10^{-3}\).
\(\int_{0}^{\pi} \sin 6 x \cos 3 x \ d x=\frac{4}{9}\)
Questions & Answers
QUESTION:
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 \(10^{-3}\).
\(\int_{0}^{\pi} \sin 6 x \cos 3 x \ d x=\frac{4}{9}\)
ANSWER: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(sin
cos
)= 2.2360679774
2 f(2 ) =4(sin
cos
)= 0.363271264
4 f( ) =4(sin
cos
)= 2.236067977
2f(4 ) =4(sin
cos
)= -1.538841769
4 f( ) =4(sin
cos
)= 0
2f( 6) =4(sin
cos
) = -1.53884176858
4 f( ) =4(sin
cos
)=2.2360679775
2f( 8) =4(sin
cos
) = 0.363271264
4 f( ) =4(sin
cos
) = 2.2360679775
f(