Integration — AS & A Level Further Mathematics (9231) questions by topic
Substitution-based integration and Riemann-sum bounding define this topic: using u = x^2 - 1 to integrate x / sqrt(x^2 - 1), using u = 1 + x^2 for a similar surd integral, and bounding an integral of (1/sqrt(x)) e^sqrt(x) between sums of rectangle areas.
Find and show are the top command words across 6 questions from 2023 to 2025 papers, worth from 5 to 12 marks, where choosing and executing the given substitution cleanly is what most of the credit rests on. With no examiner-report extracts logged for this topic, submitting each substitution or rectangle-sum derivation for instant marking is the way to confirm limits have been changed correctly before the final exact value is trusted.
May–June 2025, Paper 22
The diagram shows the curve with equation y = (1/sqrt(x)) e^(sqrt(x)) for x = 1, together with a set of n - 1 rectangles of unit width. The rectangles are positioned under (to the…
Answer this question and get it marked →May–June 2024, Paper 21
Use the substitution u = 1 + x^2 to find integral of x/sqrt(1 + x^2) dx.
Answer this question and get it marked →May–June 2024, Paper 22
Use the substitution u = 1 + x^2 to find integral of x/sqrt(1 + x^2) dx.
Answer this question and get it marked →May–June 2024, Paper 23
Find the exact value of the integral from x = 2 to x = 7/2 of 1/sqrt(4x - x^2 - 1) dx.
Answer this question and get it marked →May–June 2023, Paper 21
Use the substitution u = x^2 - 1 to find the integral of x / sqrt(x^2 - 1) with respect to x.
Answer this question and get it marked →May–June 2023, Paper 22
Use the substitution u = x^2 - 1 to find the integral of x / sqrt(x^2 - 1) dx.
Answer this question and get it marked →Other AS & A Level Further Mathematics topics
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