A-LevelMathematicsIntegration9709/12 · May/June 2021 · Q96 Marks
The diagram shows part of the curve with equation y² = x – 2 and the lines x = 5 and y = 1. The shaded region enclosed by the curve and the lines is rotated through 360° about the x-axis. Find the volume obtained. [Figure 9.1]
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Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [B1] Curve intersects y = 1 at (3, 1)
- [M1] Volume = [π][(x−2)[dx]
- [A1] [π][x²/2 – 2x] or [π][(x – 2)²/2]
- [M1] =[π][(5²/2 – 2x5)-(their 3²/2 – 2xtheir3)]
- [B1 FT] Volume of cylinder = π×1²×(5-their 3)[= 2π]
- [A1] [Volume of solid = 4 π – 2π =]2π or 6.28
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