Definite integral — Area between x and sin x

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.Integrand (upper minus lower).
Finish the calculation, then check that the result meets the question’s conditions.Primitive ; evaluate from to .
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: At : .

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