A-LevelMathematicsIntegration9709/21 · Oct/Nov 2020 · Q35 Marks
The diagram shows the curve y = 2 + e⁻²ˣ. The curve crosses the y-axis at the point A, and the point B on the curve has x-coordinate 1. The shaded region is bounded by the curve and the line segment AB. Find the exact area of the shaded region. [Figure 3.1]
- The diagram shows the curve y = 2 + e⁻²ˣ. The curve crosses the y-axis at the point A, and the point B on the curve has x-coordinate 1. The shaded region is bounded by the curve and the line segment AB. Find the exact area of the shaded region.[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.
- [M1] Integrate to obtain form ax + be^-2x
- [A1] Obtain correct 2x - (1/2)e^-2x
- [A1] Apply limits to obtain 5/2 - (1/2)e^-2
- [M1] Attempt to find area of relevant trapezium
- [A1] Obtain 5/2 + (1/2)e^-2 and subtract to obtain e^-2 or exact equivalent
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