Challenging +1.2 This is a surface area of revolution question requiring the formula S = 2π∫y√(1+(dy/dx)²)dx. While this is an FP3 topic (making it harder than standard A-level), the function is straightforward (y=2x³), the derivative is simple, and the integration, though requiring substitution, follows a standard pattern. It's above average due to being Further Maths content and requiring careful algebraic manipulation, but it's a textbook application of the formula without novel insight.
The curve \(C\) has equation \(y = 2x^3\), \(0 \leq x \leq 2\).
The curve \(C\) is rotated through \(2\pi\) radians about the \(x\)-axis.
Using calculus, find the area of the surface generated, giving your answer to 3 significant figures.
[5]
The curve $C$ has equation $y = 2x^3$, $0 \leq x \leq 2$.
The curve $C$ is rotated through $2\pi$ radians about the $x$-axis.
Using calculus, find the area of the surface generated, giving your answer to 3 significant figures.
[5]
\hfill \mbox{\textit{Edexcel FP3 2011 Q1 [5]}}