A-LevelMathematicsIntegration9709/21 · Oct/Nov 2023 · Q36 Marks
Find ∫₄¹⁰ 4/(2x-5) dx, giving your answer in the form ln a, where a is an integer.
- (a)Find ∫₄¹⁰ 4/(2x-5) dx, giving your answer in the form ln a, where a is an integer.[4]
- (b)Find the exact value of ∫₄¹⁰ e²ˣ⁻⁵ dx.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [B1] Obtain 2ln(2x-5)
- [M1] Apply limits correctly For integral of form kln(2x - 5) .
- [M1] Use one relevant logarithm property correctly For integral of form kln(2x - 5) .
- [A1] Apply second logarithm property correctly and obtain ln25
- [B1] Integrate to obtain (1/2)e²ˣ⁻⁵
- [B1FT] Obtain final answer (1/2)e¹⁵ − (1/2)e³ or exact equivalent, FT on their ke²ˣ⁻⁵.
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