A-LevelMathematicsIntegration9709/12 · May/June 2012 · Q14 Marks
The diagram shows the region enclosed by the curve y = 6/(2x-3), the x-axis and the lines x = 2 and x = 3. Find, in terms of π, the volume obtained when this region is rotated through 360° about the x-axis. [Figure 1]
- The diagram shows the region enclosed by the curve y = 6/(2x-3), the x-axis and the lines x = 2 and x = 3. Find, in terms of π, the volume obtained when this region is rotated through 360° about the x-axis.[4]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [B1 B1] Integral of y² = -36 / (2x-3) ÷ 2; co allow 2nd B1 independent of 1st.
- [M1] Use of limits 2, 3; Used as 2 to 3 or 3 to 2 in integral of y².
- [A1] → 12π or 37.7; co (uses area 0/4. No π Max 3/4)
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