A-LevelMathematicsIntegration9709/33 · Oct/Nov 2025 · Q66 Marks
Find the exact value of ∫(from 0 to π/2) x² sin 2x dx.
- (a)Find the exact value of ∫(from 0 to π/2) x² sin 2x dx.[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- Commence integration by parts and reach Ax² cos2x – ∫ Bx cos 2x dx
- Obtain –(1/2)x² cos 2x + ∫ x cos 2x dx
- Complete integration by parts and reach Ax² cos2x + Bx sin 2x + C cos 2x
- Obtain –(1/2)x² cos 2x + (1/2)x sin 2x + (1/4) cos 2x
- Substitute limits correctly in an expression of the form Ax² cos 2x + Bx sin 2x + C cos 2x and evaluate the trig expressions
- Obtain answer -1/144 π² + √3/24 π – 1/8 or exact three-term equivalent
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