Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | Q#3

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Question

The diagram shows part of the curve . The shaded region is bounded by the curve, the y- axis and the lines y = 1 and y = 2. Showing all necessary working, find the volume, in terms of ,  when this shaded region is rotated through  about the y-axis.

Solution

Expression for the volume of the solid formed when the shaded region under the curve  is rotated completely about the y-axis is;

We are given;

We can see that curve goes from 1 to 2 along y-axis.

Therefore;

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of  is:

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