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begin mathsize 14px style integral end style2 cos x sin(1 - 2x) dx = ....

  1. cos(x - 1) + begin mathsize 14px style 1 third end style cos(3x - 1) + c

  2. cos(x - 1) - begin mathsize 14px style 1 third end style cos(3x - 1) + c

  3. -sin(x - 1) + begin mathsize 14px style 1 third end style sin(3x - 1) + c

  4. -sin(x - 1) - begin mathsize 14px style 1 third end style sin(3x - 1) + c

  5. sin(x - 1) + begin mathsize 14px style 1 third end style sin(3x - 1) + c

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Ingat!

Sifat–sifat Trigonometri berikut:

2 cos α sin β = sin(α + β) - sin(α - β)

Maka:

begin mathsize 14px style integral end style2 cos x sin(1 - 2x) dx = begin mathsize 14px style integral end stylesin(x + 1 - 2x) - sin(x - (1 - 2x)) dx

                                   = begin mathsize 14px style integral end stylesin(-x + 1) - sin(3x - 1) dx

                                   = cos(-x + 1) + begin mathsize 14px style 1 third end style cos(3x - 1) + c

                                   = cos(x - 1) + begin mathsize 14px style 1 third end style cos(3x - 1) + c

423

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