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← 2024 HSC Extension 1 paper Question 13(d)

Variation 3 · answer guide

Antidifferentiation — Related substitution

Question

Using , find (hint: ).

This practice question was inspired by Question 13(d) in the 2024 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: choose a substitution or identity that simplifies the integrand, then reverse-differentiate to check. and denominator .
  2. Finish the calculation, then check that the result meets the question’s conditions.Integral .
  3. State the final answer clearly in the form the question requested.Answer: .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Similar and pattern to the exam question.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

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