MAT136H1 Lecture Notes - Trapezoidal Rule
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MAT136H1 Full Course Notes
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Question #4 (medium): integral approximation & error bound using the midpoint rule. The error bounds are given by: | | , where , and | ( )| for the midpoint. Notice that only the denominator is slightly different. | ( )( )| , 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. Sample question: given the dataset, estimate the value of the integral ( ) using the midpoint rule, if ( ) , estimate the error involved in the approximation from part 1). Solution: integral is approximated using the midpoint rule: ( ) [ ( )] Pick the midpoints (ie. every alternating points starting from the second, ending with the second last), then . Thus: ( : error bound for the midpoint rule is: | |
