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A-LevelMathematicsIntegration9709/12 · Feb/Mar 2020 · Q34 Marks

The diagram shows part of the curve with equation y = x² + 1. The shaded region enclosed by the curve, the y-axis and the line y = 5 is rotated through 360° about the y-axis. [Figure X.X]

Find the volume obtained.[4]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

[M1] (π)∫(y-1)dy SOI Attempt to integrate x² or (y-1)
[A1] (π)[y²/2 - y]
[DM1] (π)[(25/2 - 5) - (1/2 - 1)] Apply limits 1 → 5 to an integrated expression
[A1] 8π or AWRT 25.1

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About this question

Topic: Integration, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Feb/Mar 2020 Paper 1 Variant 2, question 3.

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