Volume and surface area of revolution

A question is this type if and only if it applies a reduction formula to calculate volume of revolution, surface area of revolution, or arc length of a curve.

1 questions · Challenging +1.8

Sort by: Default | Easiest first | Hardest first

CAIE FP1 2017 November Q8

11 marks Challenging +1.8

Find the value of $I _ { 2 }$.
Show that, for $n > 2$, $$( n - 1 ) I _ { n } = 2 ^ { \frac { 1 } { 2 } n - 1 } + ( n - 2 ) I _ { n - 2 }$$
The curve $C$ has equation $y = \sec ^ { 3 } x$ for $0 \leqslant x \leqslant \frac { 1 } { 4 } \pi$. The region $R$ is bounded by $C$, the $x$-axis, the $y$-axis and the line $x = \frac { 1 } { 4 } \pi$. Find the volume of revolution generated when $R$ is rotated through $2 \pi$ radians about the $x$-axis.