Nilai dari integral Π/3 sampai Π/2 (sin 3x cos 5x) dx=

integral tertentu  trogonometri
π/3
∫ sin 3x cos 5x dx =
π/2
.

π/3
∫  1/2 ( 2 sin 3x cos 5x ) dx =
π/2
.
π/3
∫ 1/2 { 2 cos 5x sin 3x) dx =
π/2
.
*ingat  rumus 2cos A sin A = sin 1/2 (A+B) - sin 1/2(A-B)*
.
π/3
∫ 1/2 { sin 1/2 (5x+3x) - sin 1/2 (5x -3x)} dx
π/2
.
π/3
∫ 1/2 { sin 4x - sin x } dx
π/2
= [1/2 (1/4 (-cos 4x) - (- cos x) )](π/3...π/2)
= [ - 1/8 cos 4x + 1/2 cos x ] π/3 ...π/2
= ( -1/8 cos 4π/3 + 1/2 cos π/3) - (- 1/8 cos 4π/2 + 1/2 cos π/2)
= (1/8 (-1/2) + 1/2 (1/2)) - ( - 1/8(1) + 1/2 (0))
= (-1/16 + 1/4 + 1/8 -0)
= 5/16