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Pertanyaan

Hasil dari ∫ sin 3 x cos x d x adalah...

Hasil dari  adalah...

  1. begin mathsize 12px style 1 half sin to the power of 4 x plus C end style

  2. begin mathsize 12px style 1 fourth sin to the power of 4 x plus C end style

  3. begin mathsize 12px style 1 over 8 sin to the power of 4 x plus C end style

  4. begin mathsize 12px style negative 1 over 8 sin to the power of 4 x plus C end style

  5. begin mathsize 12px style negative 1 half sin to the power of 4 x plus C end style

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Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

 begin mathsize 12px style integral sin cubed x cos x d x equals 1 fourth sin to the power of 4 left parenthesis x right parenthesis plus C end style

Pembahasan

Misal: u(x) = sin x du = cos x dx Maka: Jadi,

begin mathsize 12px style integral f left parenthesis g left parenthesis x right parenthesis right parenthesis times g to the power of 1 left parenthesis x right parenthesis d x  equals integral f left parenthesis u right parenthesis d u  equals integral F left parenthesis u right parenthesis plus C  equals F left parenthesis g left parenthesis x right parenthesis right parenthesis plus C  integral sin cubed x cos x d x end style

Misal:

u(x) = sin x

du = cos x dx

Maka:

begin mathsize 12px style integral sin cubed x cos x d x  equals integral u cubed d u  equals 1 fourth u to the power of 4 plus C  equals 1 fourth sin to the power of 4 left parenthesis x right parenthesis plus C end style

Jadi, begin mathsize 12px style integral sin cubed x cos x d x equals 1 fourth sin to the power of 4 left parenthesis x right parenthesis plus C end style

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