Arc length and area of a surface of revolutionEdexcel A-Level Further Maths: Mind map

Exam questions on Arc length and area of a surface of revolution

1. The curve $C$ has equation $y=\frac23x^{\frac32}$ for $x\geq0$.
   Find the exact length of the arc of $C$ from $x=0$ to $x=3$.2 marks
2. A curve is given parametrically by $x=3t^2$, $y=2t^3$ for $0\leq t\leq1$.
   Find the exact length of the curve.2 marks
3. The curve $C$ has equation $y=\sqrt{x}$ for $0\leq x\leq2$. The arc of $C$ is rotated through $2\pi$ radians about the $x$-axis to form a curved surface of area $S$.
   Show that $S=2\pi\int_0^2\sqrt{x+\frac14}\,dx$.3 marks