Variation 1 · answer guide

Inverse trigonometric functions — Denominator $9x^2+1$

Question

Which of the following is an anti-derivative of ?

This practice question was inspired by Question 3 in the 2020 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: use the restricted domain and range that make the inverse function single-valued.Write .
Finish the calculation, then check that the result meets the question’s conditions.Integrate: .
Match the result to the choices and state the correct option.Therefore option A is correct.

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

Verification: Differentiate to recover .

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