# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#2

Question

The diagram shows part of the curve  and the point P(2,3) lying on the curve. Find,  showing all necessary working, the volume obtained when the shaded region is rotated through  360about the x-axis.

Solution

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

Therefore, for the given case;

We are given that;

Hence, for x=0 and x=2;

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of  is: