Question

Kerjakan Menggunakan Langkah-langkah Pengerjaan Soal Nomor, 9, dan 10 kelas 12​

Answer 1

Verified answer

Penjelasan dengan langkah-langkah:

Integral trigonometri

9. ʃ sin² 3x dx → ( 3x = u )

dx/du = ⅓

= ⅓ ʃ sin² u du

= ⅓ ʃ ½.(1-cos(2u) du

= ⅓.½ ʃ 1-cos(2u) du

= ⅙ ( u - ½sin(2u) )

= ⅙ (3x - ½sin(6x)

= ½x - 1/12 sin(6x)

= ½x - 1/12 sin(6x) + C

10. ʃ sin³ 2x dx → ( 2x = u )

dx/du = ½

= ½ ʃ sin³ u du

= ½ ʃ sin² u.sin u du

= ½ ʃ 1 - cos² u du

= ½ ( -cos u + ⅓ cos³ u )

= -½ cos 2x + ⅙ cos³ 2x

= -½ cos 2x + ⅙ cos³ 2x + C