A-LevelMathematicsIntegration9709/23 · Oct/Nov 2023 · Q36 Marks
Find ∫ from 4 to 10 of (4 / (2x-5)) dx, giving your answer in the form ln a, where a is an integer.
- (a)Find ∫ from 4 to 10 of (4 / (2x-5)) dx, giving your answer in the form ln a, where a is an integer.[4]
- (b)Find the exact value of ∫ from 4 to 10 of e^(2x-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)e^(2x-5).
- [B1FT] Obtain final answer (1/2)e^15 - (1/2)e^3 or exact equivalent, FT on their ke^(2x-5).
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