11–12Mathematics Extension 2 11–12 Syllabus

Use the identities for trigonometric products as sums and differences to solve problems and prove results

Find indefinite integrals and evaluate definite integrals using the method of integration by substitution, where the substitution may or may not be given

Decompose rational functions whose denominators can be expressed as a product of distinct linear factors, distinct irreducible quadratic factors and perfect square factors into partial fractions

Integrate rational functions whose denominators can be expressed as a product of distinct linear factors, distinct irreducible quadratic factors and perfect square factors, using partial fraction decomposition

Integrate rational functions by completing the square on a quadratic denominator

Integrate rational functions where the degree of the numerator is not less than the degree of the denominator

Integrate functions by changing an integrand into an appropriate form using algebraic manipulation

Derive the method for integration by parts

Find indefinite integrals and evaluate definite integrals using the method of integration by parts, including problems where more than one application is required

Derive and use recurrence relations involving integration by parts

Solve theoretical problems involving multiple techniques of integration

Solve practical problems involving multiple techniques of integration