tut08 - The University of Sydney Math1003 Integral Calculus...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
The University of Sydney Math1003 Integral Calculus and Modelling Semester 2 Exercises for Week 8 2011 Assumed Knowledge Factorisation of expressions. Simple techniques of integration. Objectives (7a) To be able to recognise a di±erential equation as a separable equation. (7b ) To be able to solve a separable equation by separation of variables. (7c) To be able to perform integrations using trigonometric substitutions. Preparatory Questions 1. Which of the following di±erential equations are separable? Write those that are in separated form. ( i ) dy dx = x 2 y ( x 2 + 1) 1 / 2 ( ii ) dy dx = a 2 e y ( a 2 - x 2 ) 3 / 2 - e y ( a 2 - x 2 ) 1 / 2 ( iii ) dy dx = x + cos y x 3 x 2 - 16 . Practice Questions 2. Find the general solutions of ( i ) dy dx = 1 + y 2 ( ii ) dy dx = y cos x ( iii ) (1 + x ) dy dx + y 2 = 0 3. Evaluate the following integrals by making the given substitution: ( i ) i x 2 ( a 2 - x 2 ) 3 / 2 dx, x = a sin u .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

tut08 - The University of Sydney Math1003 Integral Calculus...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online