A-LevelMathematicsIntegration9709/32 · Oct/Nov 2021 · Q66 Marks
Using the expansions of sin(3x + 2x) and sin(3x - 2x), show that ½(sin 5x + sin x) = sin 3x cos 2x.
- (a)Using the expansions of sin(3x + 2x) and sin(3x - 2x), show that ½(sin 5x + sin x) = sin 3x cos 2x.[3]
- (b)Hence show that ∫₀^(π/4) sin 3x cos 2x dx = ½(3 - √2).[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [B1] State correct expansion of sin(3x + 2x) or sin(3x-2x)
- [M1] Substitute expansions in ½(sin 5x + sinx), or equivalent
- [A1] Simplify and obtain ½(sin 5x + sinx) = sin 3x cos 2x
- [B1] Obtain integral -1/10 cos 5x - 1/2 cos x, or equivalent
- [M1] Substitute limits correctly in an expression of the form pcos5x+qcosx
- [A1] Obtain ½(3 - √2)
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