18M.1.AHL.TZ1.H_4

pestleMathematicsAAHLPaper 118M· sl-5-11-definite-integrals-areas-under-curve-onto-x-axis-and-areas-between-curvessource ↗

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]

$\int_{ - 2}^0 {f\left( {x{\text{ + 2}}} \right){\text{d}}x}$ .

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$\int_{ - 2}^0 {f\left( x \right){\text{d}}x = 10} - 12 = - 2$ (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]

$\int_{ - 2}^0 {f\left( {x{\text{ + 2}}} \right){\text{d}}x} = \int_0^2 {f\left( x \right){\text{d}}x}$ (M1)

= 12 A1

[2 marks]

Examiners’ report

[N/A]