?Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to

Chapter 7, Problem 8

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QUESTION:

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n.

\(\int_{1}^{4} \sin \sqrt{x} \ d x, \quad n=6\)

Equation Transcription:

 sin dx,  n = 6

Text Transcription:

integral _1 ^4 sin sqrt x dx, n = 6

Questions & Answers

QUESTION:

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n.

\(\int_{1}^{4} \sin \sqrt{x} \ d x, \quad n=6\)

Equation Transcription:

 sin dx,  n = 6

Text Transcription:

integral _1 ^4 sin sqrt x dx, n = 6

ANSWER:

Step 1 of 3

(a) Trapezoid Rule

If  is divided into  subintervals, each of length , with endpoints at , then

Find the width of the intervals

Calculate the values at the interval boundaries.

Write out the Trapezoid Rule for  terms and fill in the numbers from the table.

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