The diagram shows the curve with equation $$\(y=\frac{1}{(3 x-2)^{\frac{3}{2}}}\)$$. The shaded region is bounded by the curve, the $$\(x\)$$-axis and the lines $$\(x=1\)$$ and $$\(x=2\)$$. The shaded region is rotated through $$\(360^{\circ}\)$$ about the $$\(x\)$$-axis. Find the volume of revolution. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w21_qp_11 Year：2021 Question No：10(b)
Answer:
\([\pi] \int y^{2} \mathrm{~d} x=[\pi] \int(3 x-2)^{-3} \mathrm{~d} x=[\pi] \frac{(3 x-2)^{-2}}{-2 \times 3}\)
\([\pi]\left[-\frac{1}{6}\right]\left[\frac{1}{16}-1\right]\)
\(\frac{5 \pi}{32}\)
\([\pi]\left[-\frac{1}{6}\right]\left[\frac{1}{16}-1\right]\)
\(\frac{5 \pi}{32}\)
Knowledge points:
1.8.3 evaluate definite integrals (Including simple cases of ‘improper’ integrals, such as)
1.8.4.2 a volume of revolution about one of the axes. (A volume of revolution may involve a region not bounded by the axis of rotation, e.g. the region between and y = 5 rotated about the x-axis.)
Solution:
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