A-LevelMathematicsIntegration9709/12 · May/June 2022 · Q65 Marks
The diagram shows the curve with equation y = 5x^(1/2) and the line with equation y = 2x + 2. Find the exact area of the shaded region which is bounded by the line and the curve. [Diagram]
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Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [M1] 2x + 2 = 5x^(1/2) leading to 2x - 5x^(1/2) + 2 = 0 or 4x² + 8x + 4 = 25x leading to 4x² - 17x + 4 = 0
- [A1] x = 1/4, x = 4
- [M1] Area = ∫(5x^(1/2) - (2x + 2))dx
- [DM1] Integration: [10/3 x^(3/2) - x² - 2x]
- [A1] Area = 45/16 or 2 13/16 or 2.8125
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