7.7 Integral Techniques
Question #5 (Medium): Integral Approximation & Error Bound Using Simpson’s 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.
The rate at which a scuba diver dives into the depth of the ocean at each time interval is recorded in the
1) Estimate the total depth the scuba diver reached using the Simpson’s Rule.
2) If ( ) for , estimate the error involved