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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.

Syllabus sections

Topic 6 - Calculus » 6.5 » Definite integrals, both analytically and using technology.
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