Integral batas bawah 0 dan batas atas phi/2 sin 3x cos 5x dx mohon dibantu, terimakasih

jawab

(0...π/2) ∫  sin 3x cos 5x dx
(0...π/2) ∫ { 1/2 ( 2 cos 5x  sin 3x) dx
(0..π/2) ∫ 1/2 {sin (5x+3x) - sin(5x-3x) dx
(0..π/2)  ∫ 1/2  sin 8x - 1/2 sin 2x dx
=  - 1/16  cos 8x  + 1/4 cos 2x } (π/2 ..0)
=  - 1/16 { cos 8(π/2) - cos (0)} + 1/4 {cos 2(π/2) - cos 0}
= - 1/16 { cos 4π - cos 0)   + 1/4 (cos π - cos 0)
= - 1/16 (1 - 1) + 1/4 (-1 - 1)
=  - 1/16(0) + 1/4(-2)
= 0 - 1/2
= -1/2