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2023 HSC Mathematics Extension 1

Question 12(a):
Antidifferentiation

3 marksantidifferentiation

Evaluate using the substitution .

How to recognise this question

Question type: antidifferentiation

  • The command and notation point to antidifferentiation.
  • The requested response is a worked solution.

How to handle it: choose a substitution or identity that simplifies the integrand, then reverse-differentiate to check.

Watch out: Do not select a formula until its domain, interval, sign and units match the question.

Step-by-step answer

  1. , . Bounds: ; .
  2. Integrand: .
  3. .
  4. NESA: 3 marks correct; 2 for correct anti-derivative in ; 1 for correct integrand in .

Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.

The paper records 3 total marks for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.

Try your hand at it again by answering these questions

Question 1

Evaluate using .

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Question 2

Evaluate .

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Question 3

With , evaluate .

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