The region $A$ is bounded by the curves $x^2 + y^2 = 5$ and $y = x^2 + 1$ for $y \geq 1$. Fi

Question

The region $A$ is bounded by the curves $x^2 + y^2 = 5$ and $y = x^2 + 1$ for $y \geq 1$. Find the volume when $A$ is rotated $\pi$ radians about the $y$-axis.[2] The region $B$ is bounded by the curve $y = \frac{2}{\sqrt{x^2 - 4x + 7}}$, the line $y = x - 2$, the line $x = 1$ and the $x$-axis. Find the exact volume when $B$ is rotated $2\pi$ radians about the $x$-axis. Give your answer in the form $a\sqrt{3}\pi^2 + b\pi$, where $a$ and $b$ are constants to be determined.[6]

Accepted Answer

(a)1.95 units$^3$ (b)a=$\frac{4}{9}$, b=$-\frac{1 }{3}$

2025 RVHS P2 Q3

2025 RVHS P2 Q3