A-LevelFurther MathematicsFurther CalculusOct/Nov 2014Paper 1 Q710 Marks
Let I_n = ∫₀¹ (1-x)ⁿeˣ dx. Show that, for all positive integers n, I_n = nI_(n-1) - 1. Find the exact value of I_4. By considering the area of the region enclosed by the x-axis, the y-axis and the curve with equation y = (1 – x)⁴eˣ in the interval 0 ≤ x ≤ 1, show that 1/24 < e < 11/4.
✓ Correct Answer
The correct answer is —. This question tests the candidate's understanding of further calculus 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