A-LevelMathematicsIntegration9709/33 · May/June 2021 · Q47 Marks
Let f(x) = (15-6x) / ((1+2x)(4-x))
- (a)Express f(x) in partial fractions.[3]
- (b)Hence find ∫₁² f(x) dx, giving your answer in the form ln (a/b), where a and b are integers.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] State or imply the form A/(1+2x) + B/(4-x) and use a correct method to find a constant
- [A1] Obtain one of A = 4 and B = -1
- [A1] Obtain the second value
- [B1FT] Integrate and obtain terms 2ln(1+2x)+ln(4-x)
- [M1] Substitute limits correctly in an integral of the form aln(1+2x)+bln(4−x), where ab≠0
- [A1] Obtain final answer ln (50/27)
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