7.7 Integral Techniques
Question #4 (Medium): Integral Approximation & Error Bound Using the Midpoint Rule
The error bounds are given by: | | , where , and | ( ) | for the Midpoint
Rule. Similarly for Trapezoidal Rule: | | , where , and | ( )| . Notice that
only the denominator is slightly different. As for Simpson’s Rule: | | ( ) , where , and
| ( )( ) | , meaning the fourth derivative of the function is bound by factor. Usually the question
provides these input values in order to calculate the error bounds.
1) Given the dataset, estimate the value of the integral ∫ ( ) using the Mi