Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#2

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Question

The diagram shows part of the curve  , where a is a positive constant. Given that the volume obtained when the shaded region is rotated through  about the x-axis is , find the value of .

Solution

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

For the given case;

Therefore;

Rule for integration of  is:

Therefore;

We are given that;

Therefore;

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