Matematika

Pertanyaan

Hasil integral -π sampai 1/3π cos (2x +1/3π)dx... .

1 Jawaban

  • dsin (2x + 1/3 π) /dx = 2 cos (2x + 1/3 π)
    cos (2x + 1/3 π) dx = 1/2 dsin (2x + 1/3 π)

    ∫cos (2x + 1/3 π) dx [1/3 π ... -π]
    = 1/2 ∫dsin (2x + 1/3 π)
    = 1/2 sin (2x + 1/3 π)
    = 1/2 [sin (2.(1/3 π) + 1/3 π) - sin (2(-π) + 1/3 π)]
    = 1/2 [sin π + sin 5/3 π)]
    = 1/2 [sin 180° + sin 300°]
    = 1/2 [ 0 - 1/2 √3]
    = -1/4 √3

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