A-LevelMathematicsIntegration9709/32 · Oct/Nov 2018 · Q35 Marks
Find ∫ (ln x)/x³ dx.
- (i)Find ∫ (ln x)/x³ dx.[3]
- (ii)Hence show that ∫₁² (ln x)/x³ dx = ¼(3 – ln 4).[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1*] Integrate by parts and reach a(lnx)/x² + b∫1/x³ dx
- [A1] Obtain ± (1/2)lnx/x² ± ∫ 1/(2x³) dx, or equivalent
- [A1] Complete integration correctly and obtain -lnx/(2x²) - 1/(4x²), or equivalent
- [M1(dep*)] Substitute limits correctly in an expression of the form a(lnx)/x² + b/x² or equivalent
- [A1] Obtain the given answer following full and exact working
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