2025 HSC Mathematics Extension 1
Question 11(g):
Definite integral
Evaluate .
How to recognise this question
Question type: definite integrals areas
- The command and notation point to definite integrals areas.
- The requested response is a worked solution.
How to handle it: find a suitable antiderivative, substitute the upper and lower bounds, and subtract in that order.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- .
- An antiderivative is .
- At and the sine terms vanish, leaving .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 3 total marks for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Evaluate .
Question 2
Find the area between and on .
Question 3
Evaluate .