A-LevelMathematicsIntegration9709/31 · Oct/Nov 2024 · Q25 Marks
Find the exact value of ∫ x² ln 3x dx. Give your answer in the form a lnb+c, where a and c are rational and b is an integer.
- Find the exact value of ∫ x² ln 3x dx. Give your answer in the form a lnb+c, where a and c are rational and b is an integer.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [M1*] Integrate to obtain px³ ln3x + q∫x²dx
- [A1] Obtain ⅓x³ ln3x − ⅓∫x²dx Or unsimplified equivalent.
- [A1] Complete integration to obtain ⅓x³ ln3x − ¹⁄₉x³
- [DM1] Use correct limits correctly in an expression of the form rx³ ln3x + sx³ 9ln9 - 3 - ⅓ln3 + ¹⁄₉ An exact expression for their integral.
- [A1] Obtain 53/3 ln3 - 26/9 Or 2-term equivalent.
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