Stewart Calculus, Sect 7 7 #11c Simpson's Rule | Summary and Q&A

TL;DR

Learn how to use Simpson's Scroll with n=6 to approximate an integral from 1 to 4 of the square root of 1/x.

Key Insights

• ❓ Simpson's Scroll is a numerical method used to approximate definite integrals.
• 🤯 Delta x is calculated using the formula (B - a) / N, where B is the upper limit, a is the lower limit, and N is the number of intervals.
• 🍉 The coefficients in Simpson's Rule are 1, 4, and 2, alternating between terms.
• 📈 The Y values of the function are determined using a graph or a calculator.

Transcript

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Questions & Answers

Q: What is the purpose of using Simpson's Scroll to approximate the integral?

Simpson's Scroll is used to divide the region into smaller parabolas, allowing for a more accurate approximation of the area under the curve.

Q: How is delta x calculated in the given scenario?

Delta x is calculated as (B - a) / N, where B is 4, a is 1, and N is 6. Therefore, delta x equals 0.5.

Q: What is the formula for Simpson's Rule?

The formula for Simpson's Rule is Delta x / 3 * (f(X0) + 4 * f(X1) + 2 * f(X2) + 4 * f(X3) + 2 * f(X4) + 4 * f(X5) + f(X6)).

Q: How do you determine the values of X0 to X6 for the given integral?

Start with X0 as the first number in the interval (1 in this case), and increment by delta x (0.5) to find X1, X2, and so on, until X6 is reached.

Summary & Key Takeaways

• Simpson's Scroll, with n=6, is used to approximate the integral from 1 to 4 of the square root of 1/x.

• The delta x is calculated as 0.5, which means the interval starts at 1 and increases by 0.5 units.

• The Simpson's Rule formula is applied, with specific coefficients for each term, to find the approximation of the integral.