A curve $C$ has equation $y=\frac{1}{\sqrt{4-{{x}^{2}}}}$ for $-1\le x\le 1$. The region

Question

A curve $C$ has equation $y=\frac{1}{\sqrt{4-{{x}^{2}}}}$ for $-1\le x\le 1$. The region $R$ is enclosed by $C$, the $x$- axis and the lines $x=-1$ and $x=1$. Find the exact value of the area of $R$.[3] Find the exact value of the volume generated when $R$ is rotated through two right angles about the $x$- axis.[3] Show that the volume generated when $R$ is rotated through two right angles about the $y$- axis is $\pi \,(4-2\sqrt{3})$.[4]

Accepted Answer

(i) π/3, (ii) (π/4)ln 3, (iii) π(4-2√3)

N1995 P1 Q17

N1995 P1 Q17

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