Definite integral — Different upper limit

Question

Find the area between and from to .

This practice question was inspired by Question 11(g) 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..
Finish the calculation, then check that the result meets the question’s conditions..
State the final answer clearly in the form the question requested.Answer: .

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

Verification: Same primitive, new upper bound.

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