A-LevelMathematicsIntegration9709/31 · Oct/Nov 2020 · Q1010 Marks
The diagram shows the curve y = (2 – x)e¯½ˣ, and its minimum point M. [Figure 10.1]
- (a)Find the exact coordinates of M.[5]
- (b)Find the area of the shaded region bounded by the curve and the axes. Give your answer in terms of e.[5]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- Use correct product or quotient rule
- Obtain correct derivative in any form
- Equate derivative to zero and solve for x
- Obtain x = 4
- Obtain y = -2e⁻², or exact equivalent
- Commence integration and reach a(2-x)e^(-x/2) + b∫e^(-x/2)dx
- Obtain -2(2-x)e^(-x/2) - 2∫e^(-x/2)dx
- Complete integration and obtain 2xe^(-x/2)
- Use correct limits, x = 0 and x = 2, correctly, having integrated twice
- Obtain answer 4e⁻¹, or exact equivalent
- Alternative method for question 10(b): d/dx (2xe^(-x/2)) = 2e^(-x/2) - xe^(-x/2)
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