Volumes of Revolution (Edexcel A-Level Further Mathematics): Flashcards

$V = \pi \int_a^b [y(x)]^2 \, dx$

$V = \pi \int_a^b [x(y)]^2 \, dy$

Squared radius multiplied by $\pi$

Region bounded by $y=f(x)$, x-axis, vertical lines $x=a$, $x=b$

Region bounded by $x=g(y)$, y-axis, horizontal lines $y=a$, $y=b$

Square it

$V = \pi r^2 h$

$V_{\text{composite}} = V_{\text{outer}} - V_{\text{inner}}$

In exact terms with $\pi$

The axis of rotation