A-LevelMathematicsLogarithmic and exponential functions9709/31 · May/June 2017 · Q36 Marks
It is given that x = ln(1 – y) – ln y, where 0 < y < 1.
- (i)Show that y = e⁻ˣ / (1 + e⁻ˣ).[2]
- (ii)Hence show that ∫₀¹ y dx = ln (2e / (e+1)).[4]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- Remove logarithms correctly and obtain eˣ = (1-y)/y B1
- Obtain the given answer y = e⁻ˣ / (1 + e⁻ˣ) following full working B1
- State integral kln(1+e⁻ˣ) where k = ± 1 *M1
- State correct integral -ln(1+e⁻ˣ) A1
- Use limits correctly DM1
- Obtain the given answer ln (2e / (e+1)) following full working A1
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