tut05 - 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 5 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 (4a) To understand and be able to use integration by parts to evaluate deFnite integrals. (4b ) To understand that an indeFnite integral is a function. (4c) To understand that di±erentiation and (indeFnite) integration are inverse processes when applied to functions. (4d) To be able to sketch a function deFned by an integral. (4e) To be able to derive a reduction formula for an integral. Preparatory Questions 1. ( i ) ²ind the indeFnite integral i tan x dx . Hint: Use tan x = sin x cos x and substitute u = cos x . ( ii ) Use two integration by part to Fnd the indeFnite integral i x 2 e x dx . Practice Questions 2. Evaluate the following integrals by using integration by parts.
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tut05 - The University of Sydney Math1003 Integral Calculus...

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