Variation 2 · answer guide

Definite integral — Split integral of lower curve

Question

Given , , and on , the area between and 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..
Finish the calculation, then check that the result meets the question’s conditions.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: Combine the pieces first, then subtract from .

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