?Use (a) the Midpoint Rule and (b) Simpson’s Rule to approximate the given integral with

Chapter 7, Problem 5

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QUESTION:

Use (a) the Midpoint Rule and (b) Simpson’s Rule to approximate the given integral with the specified value of n. Compare your results to the actual value to determine the error in each approximation.

\(\int_{0}^{\pi} x \sin x \ d x, \quad n=6\)

Equation Transcription:

 x sin x dx,   n = 6

Text Transcription:

integral _0 ^pi x sin x dx, n = 6

Questions & Answers

QUESTION:

Use (a) the Midpoint Rule and (b) Simpson’s Rule to approximate the given integral with the specified value of n. Compare your results to the actual value to determine the error in each approximation.

\(\int_{0}^{\pi} x \sin x \ d x, \quad n=6\)

Equation Transcription:

 x sin x dx,   n = 6

Text Transcription:

integral _0 ^pi x sin x dx, n = 6

ANSWER:

Step 1 of 6

Midpoint Rule

If  is divided into  subintervals, each of length , and  is the midpoint of the ith subinterval, then

Find the width of the intervals:

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