MATH19682

2.

(a) Let us consider the function ƒ given by ƒ(x) = √√r² – x² for a given constant r > 0.

Sketch the graph of f(x) for r < x < r. Using integration, compute the volume of

revolution obtained by rotating this graph around the x axis.

[5 marks]

(b) Let us consider the curve that is defined parametrically by

x(t) = r cos(t), y(t) = rsin(t), -

Sketch this curve, and compute its length using integration.

[5 marks]

[Total: 10 marks]