Find the volume of the solid formed when the region bounded by the graph of \(y = \sin (x - 1)\), and the lines y = 0 and y = 1 is rotated by \(2\pi \) about the y-axis.

volume \( = \pi \int {{x^2}{\text{d}}y} \)     (M1)

\(x = \arcsin y + 1\)     (M1)(A1)

volume \( = \pi \int_0^1 {{{(\arcsin y + 1)}^2}{\text{d}}y} \)     A1

Note:A1 is for the limits, provided a correct integration of y.

\( = 2.608993 \ldots \pi  = 8.20\)     A2     N5

[6 marks]

Although it was recognised that the imprecise nature of the wording of the question caused some difficulties, these were overwhelmingly by candidates who were attempting to rotate around the \(x\)-axis. The majority of students who understood to rotate about the \(y\)-axis had no difficulties in writing the correct integral. Marks lost were for inability to find the correct value of the integral on the GDC (some clearly had the calculator in degrees) and also for poor rounding where the GDC had been used correctly. In the few instances where students seemed confused by the lack of precision in the question, benefit of the doubt was given and full points awarded.