| Date | November 2013 | Marks available | 4 | Reference code | 13N.1.sl.TZ0.4 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
Consider a function \(f(x)\) such that \(\int_1^6 {f(x){\text{d}}x = 8} \).
Find \(\int_1^6 {2f(x){\text{d}}x} \).
[2]
a.
Find \(\int_1^6 {\left( {f(x) + 2} \right){\text{d}}x} \).
[4]
b.
Markscheme
appropriate approach (M1)
eg \(2\int {f(x),{\text{ }}2(8)} \)
\(\int_1^6 {2f(x){\text{d}}x = 16} \) A1 N2
[2 marks]
a.
appropriate approach (M1)
eg \(\int {f(x) + \int {2,{\text{ }}8 + \int 2 } } \)
\(\int {2{\text{d}}x = 2x} \) (seen anywhere) (A1)
substituting limits into their integrated function and subtracting (in any order) (M1)
eg \(2(6) - 2(1),{\text{ }}8 + 12 - 2\)
\(\int_1^6 {\left( {f(x) + 2} \right){\text{d}}x = 18} \) A1 N3
[4 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
