(a) ∫ sin^2 3x cos⁡ 3x dx (b) ∫ cos⁡ x dx / √(sin⁡x ) tentukan integralnya

Posted by andi telaumbanua on Feb 17, 2018 in Matematika |
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Tentukanlah integral berikut:

  1. ∫ sin^2 3x cos⁡ 3x dx

  2. ∫ cos⁡ x dx / √(sin⁡x )

Jawab:

1. Misalkan: u = sin 3x

Maka: du/dx=3cos⁡3x

Sehingga : dx = du/(3 cos⁡3x )

Atau: cos 3x dx = du/3

∫ sin^2 3x cos⁡ 3x dx = ∫ u^2 cos⁡ 3x du / (3 cos⁡3x ) =  1/3 ∫ u^2 du = 1/3 1/3 u^3 +  c = 1/9 (sin 3x)^3  +  C

2. Misalkan: u = sin x

Maka: du/dx = cos⁡x

Sehingga : dx = du/cos⁡x

∫ cos⁡ x dx /√(sin⁡x ) = ∫ (cos⁡x ) /(u)^(1/2) du/cos⁡x = ∫ (u)^(-1/(2 )) du = 1/(- 1/2+ 1) u^(1/2) +  C = 2 √u + C = 2 √(sin⁡x ) +  C

 

 

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Tentukanlah integral berikut:

1. ∫ sin^2 3x cos⁡ 3x dx

2. ∫ cos⁡ x dx / √(sin⁡x)

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