18 5. (i) Evaluate the improper integral 2 1 1 2 e d ∞ − ∫ x x (3) (ii) The air temperature, θ °C, on a particular day in London is modelled by the equation θ = 8 – 5 sin 12 π t – cos 6 π t 0 t 24 where t is the number of hours after midnight. (a) Use calculus to show that the mean air temperature on this day is 8 °C, according to the model. (3) Given that the actual mean air temperature recorded on this day was higher than 8 °C, (b) explain how the model could be refined. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
Get full Socratic AI guidance on this question — free in the Applaa desktop app
Appy Buddy guides you step-by-step toward the answer without giving it away. Type your attempt and get instant, mark-scheme-aware clues that teach you to think like an examiner.
Join Applaa Community
Create your own games, learn AI concepts, program interactive apps, and share with a kid-safe community approved by parents. Free forever on Windows and Mac.
Available for Windows and macOS · COPPA Compliant
Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
While Other Kids Get an AI Head Start, Is Yours Falling Behind?
Give your child the same AI app-building, exam prep and tutoring edge — free for the first month, no credit card needed.
Join 10,000+ students building their first AI-powered apps with Applaa