tut09 - 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 9 2011 Assumed Knowledge Integration techniques. Objectives (8a) To be able to write a rational expression as a sum of partial fractions. (8b ) To be able to solve a separable equation using partial fractions. Preparatory Questions 1. Use partial fractions to express the following as a sum of terms: ( i ) 1 ( x + 1)( x - 2) ( ii ) 7 2 x 2 + 5 x - 3 ( iii ) 1 ( x + a )( x + b ) ( iv ) x x - 5 Practice Questions 2. Evaluate the integrals: ( i ) i 1 ( x + 1)( x - 2) dx ( ii ) i 7 2 x 2 + 5 x - 3 dx ( iii ) i 1 ( x + a )( x + b ) dx ( iv ) i x x - 5 dx 3. (Suitable for group work and discussion.) A trout farmer believes that, if she doesn’t remove any Fsh from a certain tank, the population of Fsh is modelled by the di±erential equation dP dt = 2 P - 0 . 01 P 2 , where P is the number of Fsh after t years. ( i ) Suppose the farmer initially stocks the tank with 50 Fsh.
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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.

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tut09 - The University of Sydney Math1003 Integral Calculus...

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