Paper 1 October/November 2009 MATHEMATICH (9709/11) A Levels
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The diagram shows part of the curve $y = \frac{1}{{{{\left( {3x + 1} \right)}^{\frac{1}{4}}}}}$. The curve cuts the y-axis at $A$ and the line $x = 5$ at $B$.
a) Show that the equation of the line $AB$ is $y = - \frac{1}{{10}}x + 1$.
b) Find the volume obtained when the shaded region is rotated through ${360^ \circ }$ about the x-axis.