Date | May 2015 | Marks available | 2 | Reference code | 15M.1.hl.TZ1.3 |
Level | HL only | Paper | 1 | Time zone | TZ1 |
Command term | Find | Question number | 3 | Adapted from | N/A |
Question
Find \(\int {(1 + {{\tan }^2}x){\text{d}}x} \).
[2]
a.
Find \(\int {{{\sin }^2}x{\text{d}}x} \).
[3]
b.
Markscheme
\(\int {(1 + {{\tan }^2}x){\text{d}}x} = \int {{{\sec }^2}x{\text{d}}x = \tan x( + c)} \) M1A1
[2 marks]
a.
\(\int {{{\sin }^2}x{\text{d}}x} = \int {\frac{{1 - \cos 2x}}{2}{\text{d}}x} \) M1A1
\( = \frac{x}{2} - \frac{{\sin 2x}}{4}( + c)\) A1
Note: Allow integration by parts followed by trig identity.
Award M1 for parts, A1 for trig identity, A1 final answer.
[3 marks]
Total [5 marks]
b.
Examiners report
Some correct answers but too many candidates had a poor approach and did not use the trig identity.
a.
Same as (a).
b.