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.
✓ Correct Answer
The correct answer is —. This question tests the candidate's understanding of vectors within the Further Mathematicssyllabus. The examiner's mark scheme requires...
📋 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...
🔒
Unlock the Examiner's Answer
Sign up for free to reveal the correct answer, the official mark scheme breakdown, and the examiner trap analysis for this question.
Sign Up Free to Unlock →Join thousands of Cambridge students already using Oracle Prep