Variation 3 · answer guide

Definite integral — When net integral fails

Question

If but on a set of positive measure, the total area between the curves is

This practice question was inspired by Question 2 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.

Set up the solution: find a suitable antiderivative, substitute the upper and lower bounds, and subtract in that order.Net signed area zero means positive and negative lobes cancel.
Finish the calculation, then check that the result meets the question’s conditions.Absolute area is still strictly positive.
Match the result to the choices and state the correct option.Therefore option B is correct.

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

Verification: Classic example: and on has net integral but area .

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