Variation 3 · answer guide
Definite integral — An exact exponential area
Question
Evaluate .
This practice question was inspired by Question 11(g) in the 2025 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Step by step
- Set up the solution: find a suitable antiderivative, substitute the upper and lower bounds, and subtract in that order.An antiderivative is .
- Simplify the previous line carefully, keeping exact values where possible.Substitute the bounds: .
- Finish the calculation, then check that the result meets the question’s conditions.Since , the result is .
- State the final answer clearly in the form the question requested.Final answer:
Common mistake: changing so many features that the new example no longer tests the same mathematical idea.
Verification: A numerical estimate of the increasing positive integrand is consistent with .
Any mark labels are a TestMum study aid, not an official NESA marking allocation.
← Back to 2025 HSC Extension 1 paper Question 11(g)