Matematika

Pertanyaan

No
1. Salah satu nilai k yangmemenuhi persamaan k integral 2 (2x-1) dx=4 adalah.....

2. 2 integral 0 (x+3)(2x-1) dx adalah...

3. Hasil dari 2integral 1 (x^2 - 1/x^2) dx adalah

1 Jawaban

  • 1) (2x - 1) dx = 4
    x² - x = 4
    k² - k - (2² - 2) = 4
    k² - k - 2 = 4
    k² - k - 6 = 0
    (k - 3)(k + 2) = 0
    k = 3 atau k = -2
    2) (x + 3)(2x - 1)dx
    = (2x² + 5x - 3) dx
    = (2/3)x³ + (5/2)x² - 3x
    = (2/3)(2³) + (5/2)(2)² - 3(2) - {(2/3)0³ + (5/2)0² - 3(0)}
    = 16/3 + 20/2 - 6 - {0}
    = 16/3 + 10 - 6
    = 16/3 + 4
    = 16/3 + 12/3
    = 28/3
    = 9⅓
    3) (x² - 1/x²) dx
    (x² - x^-2) dx
    = ⅓x³ + x^-1
    = ⅓x³ + 1/x
    = ⅓(2³) + 1/2 - {⅓(1³) + 1/1)}
    = 8/3 + 1/2 - {⅓ + 1}
    = 8/3 + 1/2 - ⅓ - 1
    = 7/3 + 1/2 - 1
    = 14/6 + 3/6 - 6/6
    = 11/6
    = 1(5/6)

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