NSW Syllabuses

# Mathematics Extension 2 Stage 6 - Year 12 Extension 2 - Calculus MEX-C1 Advanced Calculus Skills

## Outcomes

#### A student:

• MEX12-1

understands and uses different representations of numbers and functions to model, prove results and find solutions to problems in a variety of contexts

• MEX12-5

applies techniques of integration to structured and unstructured problems

• MEX12-7

applies various mathematical techniques and concepts to model and solve structured, unstructured and multi-step problems

• MEX12-8

communicates and justifies abstract ideas and relationships using appropriate language, notation and logical argument

## Subtopic Focus

The principal focus of this subtopic is extending students’ knowledge, understanding and skills to a broader range of integration techniques, such as integration of rational functions, integration using partial fractions and integration by parts.

Students develop the ability to recognise and apply this knowledge in a variety of contexts and multi-step problems.

## Content

• Students:
• integrate rational functions involving a quadratic denominator by completing the square or otherwise
• integrate rational functions whose denominators have simple linear or quadratic factors or a combination of both
• use partial fractions to integrate functions of the form $$\frac{f(x)}{g(x)}$$, where $$f(x)$$ and $$g(x)$$ are polynomials and $$g(x)$$ is expressed in simple linear or quadratic factors (ACMSM122)
• evaluate integrals using the method of integration by parts  (ACMSM123)
• develop the method for integration by parts, $$\int uv'\,dx = uv - \int vu' \,dx$$, where $$u$$ and $$v$$ are both functions of $$x$$
• apply these techniques of integration to practical and theoretical situations