2013澳大利亚高考数学试题答案(9)

Question 13 (15 marks) Use a SEPARATE writing booklet.

1

n

(a) Let I

n = 1 x2 )2 dx,

where n ≥ 0 is an integer. 0

((i) Show that I n = nn + 1 I n 2

for every integer n ≥ 2. (ii) Evaluate I5.

(b) The diagram shows the graph of a function (x).

Sketch the following curves on separate half-page diagrams. (i) y2 = (x ) (ii) y =

1 1 x

Question 13 continues on page 11

3 2

2 3