TestMum
← 2023 HSC Extension 1 paper Question 12(a)

Variation 1 · answer guide

Antidifferentiation — Shifted bounds

Question

Evaluate using .

This practice question was inspired by Question 12(a) in the 2023 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., bounds to ; integrand .
  2. State the final answer clearly in the form the question requested..

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

Verification: Same structure as the paper with different linear factor.

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

← Back to 2023 HSC Extension 1 paper Question 12(a)