The diagram below shows the curve with equation $y={{x}^{2}}-1$, $x0$ and the tangent $y=2x-2$ to t

Question

The diagram below shows the curve with equation $y={{x}^{2}}-1$, $x>0$ and the tangent $y=2x-2$ to the curve at the point $(1,0)$. Write down the coordinates of the point where this tangent meets the line $x=3$. [1] The region, $R$, shaded in the diagram, is bounded by the curve, the tangent to the curve at $(1,0)$ and the line $x=3$. Find the area of $R$, [2] the exact volume of the solid of revolution obtained when $R$ is rotated through $2\pi $ radians about the $y$-axis. [4]

Accepted Answer

$\frac{40\pi}{3}$ units³

2011 CJC P1 Q8

2011 CJC P1 Q8

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