A-LevelMathematicsIntegration9709/33 · May/June 2018 · Q35 Marks
Showing all necessary working, find the value of ∫(from 0 to π/3) x cos 3x dx, giving your answer in terms of π.
- Showing all necessary working, find the value of ∫(from 0 to π/3) x cos 3x dx, giving your answer in terms of π.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- M1* Integrate by parts and reach axsin3x + b∫sin3xdx
- A1 Obtain (1/3)xsin3x - (1/3)∫sin3xdx, or equivalent
- A1 Complete the integration and obtain (1/3)xsin3x + (1/9)cos3x, or equivalent
- M1(dep*) Substitute limits correctly having integrated twice and obtained ax sin 3x + b cos 3x
- A1 Obtain answer (1/18)(π-2) OE
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