Variation 1 · answer guide

Definite integral — Always-positive gap

Question

If , and on , the area between the curves is

This practice question was inspired by Question 4 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.

Set up the solution: find a suitable antiderivative, substitute the upper and lower bounds, and subtract in that order.Area .
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: Do not add the integrals when computing area between curves.

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