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

Chapter 7, Problem 9

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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 \(n\).

\(\int_{0}^{1} \sqrt{e^{x}-1} d x, \quad n=10\)

Equation Transcription:

Text Transcription:

n

int_{0}^{1} sqrt{e^{x}-1} d x,  n = 10

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 \(n\).

\(\int_{0}^{1} \sqrt{e^{x}-1} d x, \quad n=10\)

Equation Transcription:

Text Transcription:

n

int_{0}^{1} sqrt{e^{x}-1} d x,  n = 10

ANSWER:

Step 1 of 5

(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.

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