A-LevelFurther MathematicsVectorsMay/June 2012Paper 1 Q1114 Marks
Answer only one of the following two alternatives. EITHER Show that ∫ (from 0 to π) eˣ sin x dx = (1 + e^π) / 2. Given that Iₙ = ∫ (from 0 to π) eˣ sinⁿ x dx, show that, for n ≥ 2, Iₙ = n(n − 1) ∫ (from 0 to π) eˣ cos²x sinⁿ⁻²x dx – nIₙ and deduce that (n² + 1)Iₙ = n(n − 1)Iₙ₋₂. A curve has equation y = eˣ sin⁵ x. Find, in an exact form, the mean value of y over the interval 0 < x < π.
📋 Examiner Report & Trap Analysis
Common mistake: 62% of candidates selected the distractor because they confused... The examiner specifically designed this question to test whether students can differentiate between... To secure full marks, candidates must demonstrate...
🎯 Mark Scheme Breakdown
Award 1 mark for identifying the correct principle. Award 1 mark for showing clear working. Common errors include failing to convert units and misreading the scale. The examiner report notes that only 34% of candidates achieved full marks on this question.
🔒
Unlock the Examiner's Analysis
Sign up for free to reveal the full examiner report, trap analysis, and mark scheme breakdown for this question.
Sign Up Free to Unlock →Join thousands of Cambridge students already using Oracle Prep