Error Bound Formulas for midpoint and trapezoid rules, sect7.7#19b  Summary and Q&A
TL;DR
Learn how to use error formulas to approximate integrals using the trapezoid and midpoint rules, with examples and calculations.
Questions & Answers
Q: What are the formulas for estimating the error in the trapezoid and midpoint rules?
The formula for the trapezoid rule is E(T) = ((ba)^3/(12n^2)) * K, while the formula for the midpoint rule is E(M) = ((ba)^3/(24n^2)) * K, where K is the maximum value of the absolute value of the second derivative.
Q: How do you determine the K value?
To determine the K value, you need to find the maximum value of the absolute value of the second derivative of the function being integrated. This can be done by graphing the function on a graphing calculator and using the calculator's maximum function.
Q: What are A and B in the error formulas?
A and B represent the limits of integration. A is the starting value, while B is the ending value. In the provided example, A is 0 and B is 1.
Q: Why is it important to find the K value accurately?
Finding the K value accurately ensures a more precise estimation of the error in the approximation. Using a more accurate K value improves the reliability of the calculated error in both the trapezoid and midpoint rules.
Summary & Key Takeaways

The content explains how to use error formulas to approximate integrals using the trapezoid and midpoint rules.

It discusses the formulas for estimating the error in both methods, emphasizing their similarities and differences.

The video demonstrates stepbystep calculations and provides explanations for finding the maximum value of the second derivative to determine the K value.