A-LevelFurther MathematicsIntegration9231/12 · May/June 2018 · Q15 Marks
The curve C is defined parametrically by x = eᵗ - t, y = 4e½ᵗ. Find the length of the arc of C from the point where t = 0 to the point where t = 3.
- The curve C is defined parametrically by x = eᵗ - t, y = 4e½ᵗ. Find the length of the arc of C from the point where t = 0 to the point where t = 3.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- B1 dx/dt = e^t - 1 and dy/dt = 2e^(t/2)
- M1 M1 for using (ds/dt)^2 = (dx/dt)^2 + (dy/dt)^2
- A1 (dx/dt)^2 + (dy/dt)^2 = (e^t + 1)^2
- M1 M1 for good attempt at correct integral
- A1 = 2 + e^3 (or 22.1)
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