integral 0 sampai 45 sin 5x sin x dx=...

jawab

₀∫⁴⁵°  sin 5x sin x dx =

= ₀∫⁴⁵°  -1/2 (-2 sin 5x sin x) dx
= - 1/2 ₀∫⁴⁵°  (-2 sin 5x sin x) dx
= -1/2 [ cos 6x - cos 4x]⁴⁵₀
= - 1/2 [ 1/6 sin 6x - 1/4 sin 4x ]⁴⁵₀
= -1/12 sin 6x + 1/8 si 4x ]⁴⁵₀
= -1/12 (sin 270 - sin 45) + 1/8 (sin 45 - sin 0)
= -1/12 (-1 - 1/2√2) + 1/8 (1/2√2- 0)
= 1/12 + 1/24 + 1/16 √2