Find $\int_1^6 {2f(x){\text{d}}x}$.

Find $\int_1^6 {\left( {f(x) + 2} \right){\text{d}}x}$.

appropriate approach     (M1)

eg     $2\int {f(x),{\text{ }}2(8)}$

$\int_1^6 {2f(x){\text{d}}x = 16}$     A1     N2

[2 marks]

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]