Penyelesaian ₀∫π/64sin7xcos3x dx dengan menggunakan rumus:
2 sinα cosβ = sin(α + β) + sin(α – β)
Jawab:
₀∫π/64 sin 7x cos 3x dx
= 2 ₀∫π/6 sin(7x + 3x) + sin (7x – 3x)dx
= 2 ₀∫π/6 (sin 10x + sin 4x) dx
= 2 [ –1 cos 10x – 1 cos 4x ]₀π/6
10 4
10 4
= (-1 cos 10π – 1 cos 4π) – (-1 cos 0 – 1 cos 0)
5 6 2 6 5 2
= (-1 cos 300° – 1 cos 120° ) – (-1 . 1 – 1 . 1)
5 2 5 2
= (- 1 . 1 – 1 (- 1) + 1 + 1
5 2 2 2 5 2
= (- 4 + 10 + 8 + 20)
40 40 40 40
= 34
40
= 17
20