Solution Found!
Answer: Using Simpson’s Rule Approximate the following
Chapter 5, Problem 46E(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 \(10^{-3}\).
\(\int_{0}^{\pi} \ln (2+\cos x) d x=\pi \ln \left(\frac{2+\sqrt{3}}{2}\right)\)
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 \(10^{-3}\).
\(\int_{0}^{\pi} \ln (2+\cos x) d x=\pi \ln \left(\frac{2+\sqrt{3}}{2}\right)\)
ANSWER: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