O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2020 · Q89 Marks
Show that 3/(2x-3) + 3/(2x+3) can be written as 12x / (4x²-9).
- (a)Show that 3/(2x-3) + 3/(2x+3) can be written as 12x / (4x²-9).[2]
- (b)Hence find ∫ 12x/(4x²-9) dx, giving your answer as a single logarithm and an arbitrary constant.[3]
- (c)Given that ∫_2^a 12x/(4x²-9) dx = ln 5√5, where a > 2, find the exact value of a.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] Must see for M1
- [A1] 12x / (4x²-9)
- [B2] For each correct term, having made use of (a)
- [B1] 3/2 ln(4x²-9)+c or 3/2 ln((2x-3)(2x+3))+c or 3/2 ln(4x^2-9)^2+c
- [M1] For correct application of limits, allow equivalent forms
- [A1] For a correct method of dealing with logarithms and eliminating them
- [M1] For solving a quadratic equation, dep on first M mark
- [A1] a = √11
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