- [Maximum mark: 9]
Consider the function f(x) = x√3 − x², −√3 ≤ x ≤ √3.
(a) Sketch the graph of y = f(x) on the following pair of axes. [2]
The area between the graph of y = f(x) and the x‑axis is rotated through 360° about the x‑axis.
(b) (i) Write down an integral that represents this volume.
(ii) Calculate the value of this integral. [4]
The graph of the function f is transformed, to give the graph of the function g, in the following way:
• It is first stretched by scale factor 2, parallel to the x‑axis with the y‑axis invariant.
• It is then stretched by scale factor 0.5, parallel to the y‑axis with the x‑axis invariant.
(c) Find the volume obtained when the area between the graph of y = g(x) and the x‑axis is rotated through 360° about the x‑axis. [3]