Definite integral — Area with cos upper curve

Question

Find the area between and from to the first positive intersection is not required; instead evaluate .

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.Primitive .
Finish the calculation, then check that the result meets the question’s conditions.At : ; at : .
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: Check on .

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