A-LevelMathematicsIntegration9709/31 · Oct/Nov 2017 · Q89 Marks
Let f(x) = (4x² + 9x - 8) / ((x + 2)(2x - 1))
- (i)Express f(x) in the form A + B/(x+2) + C/(2x-1)[4]
- (ii)Hence show that ∫₁⁴ f(x) dx = 6 + ½ln(⁴⁸/₅).[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [M1] (i) Use a relevant method to determine a constant
- [A1] (i) Obtain one of the values A = 2, B = 2, C = −1
- [A1] (i) Obtain a second value
- [A1] (i) Obtain the third value
- [B2 FT] (ii) Integrate and obtain terms 2x + 2ln(x + 2) − ½ln(2x − 1) (deduct B1 for each error or omission) [The FT is on A, B and C]
- [*M1] (ii) Substitute limits correctly in an integral containing terms a ln(x + 2) and b ln(2x − 1), where ab ≠ 0
- [DM1] (ii) Use at least one law of logarithms correctly
- [A1] (ii) Obtain the given answer after full and correct working
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