# tut02 - The University of Sydney Math1003 Integral Calculus...

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The University of Sydney Math1003 Integral Calculus and Modelling Semester 2 Exercises for Week 2 2011 Assumed Knowledge Sigma notation for sums. The ideas of a sequence of numbers and of the limit of a sequence. Sketching a representative graph of a function given a formula or a set of tabulated values. Objectives (1a) To know what is meant by a Riemann sum. (1b) To understand the deFnition of the deFnite integral of a function as the limit of a Riemann sum. (1c) To understand how to interpret a deFnite integral of a function in terms of area when the function is not always positive. (1d) To be able to use the upper and lower sums to obtain an estimate of the error in evaluating a deFnite integral. (1e) To be able to Fnd the number of subintervals (sampling frequency) required to reduce the error to a given value in the case of monotonic functions. Preparatory Questions 1. ( i ) Evaluate the sum 4 s k =0 ( - 1) k k + 2 . ( ii

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tut02 - The University of Sydney Math1003 Integral Calculus...

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