Question

1..Hasil dari integral ( sin 2x +3 cos x) dx =
2..hasil integral ( sin 3x+cos x) dx =

buat kakak kakak tolong bntuin ea coz penting bnget nie gue

Answer 1

Bab Integral
Matematika SMA Kelas XII

Perhatikan,
∫ sin ax dx = - ¹/ₐ.cos ax + c
∫ cos ax dx = ¹/ₐ.sin ax + c

[1]  
⇔ ∫ [sin 2x + 3 cos x] dx

⇔ = - ¹/₂.cos 2x + 3 sin x + c

∴  ∫ [sin 2x + 3 cos x] dx = - ¹/₂.cos 2x + 3 sin x + c

[2]    π  
⇔ ₀ ∫   [sin 3x + cos x] dx

⇔ = [- ¹/₃.cos 3x + sin x]

⇔ = [- ¹/₃.cos 3π + sin π] - [- ¹/₃.cos 3(0°) + sin 0°]

⇔ = [- ¹/₃.cos 540° + sin 180°] - [- ¹/₃.cos 0° + sin 0°]

⇔ = [- ¹/₃.(- 1) + 0] - [- ¹/₃.(1) + 0]

⇔ = ¹/₃ + ¹/₃

∴     π  
    ₀ ∫   [sin 3x + cos x] dx = ²/₃