| Date | May 2018 | Marks available | 4 | Reference code | 18M.1.hl.TZ1.4 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
Given that \(\int_{ - 2}^2 {f\left( x \right){\text{d}}x = 10} \) and \(\int_0^2 {f\left( x \right){\text{d}}x = 12} \), find
\(\int_{ - 2}^0 {\left( {f\left( x \right){\text{ + 2}}} \right){\text{d}}x} \).
[4]
a.
\(\int_{ - 2}^0 {f\left( {x{\text{ + 2}}} \right){\text{d}}x} \).
[2]
b.
Markscheme
\(\int_{ - 2}^0 {f\left( x \right){\text{d}}x = 10} - 12 = - 2\) (M1)(A1)
\(\int_{ - 2}^0 {2{\text{d}}x = \left[ {2x} \right]} _{ - 2}^0 = 4\) A1
\(\int_{ - 2}^0 {\left( {f\left( x \right){\text{ + 2}}} \right){\text{d}}x} = 2\) A1
[4 marks]
a.
\(\int_{ - 2}^0 {f\left( {x{\text{ + 2}}} \right){\text{d}}x} = \int_0^2 {f\left( x \right){\text{d}}x} \) (M1)
= 12 A1
[2 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
