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Unformatted text preview: The University of Sydney Math1003 Integral Calculus and Modelling Semester 2 Exercises for Week 4 2011 Assumed Knowledge Sketching curves of simple functions. Integrals of simple functions such as x n (including 1 /x ), sin x , cos x , e x . Objectives (3a) To be able to interpret an area or volume as the limit of an appropriate Riemann sum. (3b) To be able to use elementary slices to construct Riemann sums for areas and volumes. (3c) To be able to use elementary shells to construct Riemann sums for volumes. (3d ) To understand the substitution formula and be able to use simple substitutions to evaluate definite integrals. Preparatory Questions 1. Evaluate the following definite integrals: ( i ) integraldisplay 5 cos parenleftBig x 10 parenrightBig dx . ( ii ) integraldisplay 2 1 x- 1 dx . ( iii ) integraldisplay 1 x dx . 2. Sketch the region bounded by the curves y = sin x and y = sin 2 x , and the straight lines x = 0 and x = / 2....
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This note was uploaded on 09/01/2011 for the course YEAR 1 taught by Professor Various during the Three '11 term at University of Sydney.
- Three '11