2025 HSC Mathematics Extension 1
Question 3:
Trigonometric substitution
Consider . The substitution is applied. Which of the following is obtained?
How to recognise this question
Question type: trigonometric substitution
- The command and notation point to trigonometric substitution.
- The requested response is a multiple choice.
How to handle it: write the substitution, its derivative and the new limits before simplifying.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- With , and .
- The endpoints become .
- After cancellation the integrand is , so option B is correct.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark 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
Using , evaluate .
Question 2
Using , evaluate .
Question 3
Evaluate .