A-LevelMathematicsIntegration9709/32 · Feb/Mar 2021 · Q67 Marks
Let f(x) = 5a / ((2x – a)(3a – x)), where a is a positive constant.
- (a)Express f(x) in partial fractions.[3]
- (b)Hence show that ∫ (from a to 2a) f(x) dx = ln 6.[4]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.
- [M1] Carry out a relevant method to determine constants A and B such that 5a / ((2x-a)(3a-x)) = A / (2x-a) + B / (3a-x)
- [A1] Obtain A = 2
- [A1] Obtain B = 1
- [B1 FT] Integrate and obtain terms ln(2x-a)
- [B1 FT] Integrate and obtain terms -ln(3a-x)
- [M1] Substitute limits correctly in a solution containing terms of the form b ln(2x-a) and c ln(3a-x), where bc ≠ 0
- [A1] Obtain the given answer showing full and correct working
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