A-LevelMathematicsIntegration9709/22 · Oct/Nov 2023 · Q35 Marks
The diagram shows the curve with equation y = 6e⁻¹/²x. The points on the curve with x-coordinates 0 and 2 are denoted by A and B respectively. The shaded region is enclosed by the curve, the line through A parallel to the x-axis and the line through B parallel to the y-axis. [Figure 3.1]
- (a)Find the exact gradient of the curve at B.[2]
- (b)Find the exact area of the shaded region.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [M1] (a) Differentiate to obtain form ke^(–½x) For any non-zero k except 6.
- [A1] (a) Substitute x=2 to obtain -3e⁻¹ or -3/e
- [B1] (b) Integrate to obtain -12e^(–½x) OE
- [M1] (b) Use limits 0 and 2 correctly to an integral of the form ke^(–½x), retaining exactness For any non-zero k except 6 or equivalent perhaps involving integration of 6 - 6e^(–½x).
- [A1] (b) Subtract from 12 to obtain final answer 12e⁻¹ or 12/e
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