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# tut03 - 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 3 2011 Assumed Knowledge Integrals of simple functions such as x n (including 1 /x ), sin x , cos x , e x . The simple properties of definite integrals. Objectives (2a) To be able to estimate the definite integral of a function and the error of the estimate using Riemann sums. (2b) To be able to estimate a sum of a series by comparing it with a definite integral. (2c ) To understand that integration and differentiation are inverse operations, i.e. that the definite integral of the derivative of a function is equal to the difference between the function values at the end-points, integraltext b a F ( x ) dx = F ( b ) - F ( a ). (2d) To understand the conditions under which the definite integral of a function exists. (2e) To be able to use the properties of definite integrals confidently. Preparatory Questions 1. Let f and g be continuous functions on the interval [ a,b ], and let a c b .

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tut03 - The University of Sydney Math1003 Integral Calculus...

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