← Maths Extension 2 syllabus

NSWMaths Extension 2

Further Integration (MEX-C1)

3 dot points across 3 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How does integration by parts reverse the product rule, and how do we choose the parts to evaluate products such as $x e^x$ or $x \ln x$ ?

Apply integration by parts to evaluate integrals of products, including repeated application and the recovery of the original integral
A focused answer to the HSC Maths Extension 2 dot point on integration by parts. The formula, choosing the parts with LIATE, repeated application, and the boomerang case where the original integral reappears, with verified worked examples.
6 min answer →

How does decomposing a rational function into partial fractions turn an awkward integral into a sum of standard logarithm and arctangent integrals?

Decompose rational functions into partial fractions and use the decomposition to integrate, including linear, repeated and irreducible quadratic factors
A focused answer to the HSC Maths Extension 2 dot point on partial fractions. Decomposing proper rational functions over distinct linear, repeated and irreducible quadratic factors, then integrating to logs and arctangents, with verified worked examples.
6 min answer →

How do trigonometric and rationalising substitutions transform integrals containing square roots or awkward rational functions into standard forms?

Evaluate integrals using trigonometric substitution and the t = tan(x/2) substitution, including completing the square to reach standard inverse-trigonometric and logarithmic forms
A focused answer to the HSC Maths Extension 2 dot point on substitution integration. Trigonometric substitutions for square roots, completing the square to standard forms, and the t = tan(x/2) substitution for rational trigonometric integrals, with verified worked examples.
6 min answer →