# 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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