(i)[6]
Show that $B$ is the mid-point of $AP$.
(ii)[5]
Find, showing all necessary working, the exact volume formed when the shaded region is rotated through $360^\circ$ about the $y$-axis.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram illustrates part of the curve $y = \sqrt{9 - 2x^2}$. Point $P(2, 1)$ is on the curve, and the normal at $P$ cuts the $x$-axis at $A$ and the $y$-axis at $B$. The shaded area is enclosed by the curve, the $y$-axis and the line $y = 1$.