Matematika

Pertanyaan

beserta caranya kalau bisa
beserta caranya kalau bisa

1 Jawaban

  • No. 18
    Misal
    u = 1 - 2x²
    du = -4x dx
    -du/4 = x dx

    Jadi integral dapat ditulis
    -3/4 ∫ √u  du
    = -3/4 (2/3) u^(3/2) + c
    = (-1/2) u^(3/2) + c
    = (-1/2) (1-2x²)^(3/2) + c   ==>  D

    Nomor 19
    Misal 
    u = sin x
    du = cos x dx
    Maka ∫ sin⁴x  cos x  dx
    = ∫ u⁴ du
    = u⁵/5 + c
    = (1/5)sin⁵x + c   ==> A

    Nomor 20
    Misal
    u = x³ + 1
    du = 3x² dx
    du/3 = x² dx
    Jangan lupa mengubah batas integral
    u = x³ + 1
    u = 1 + 1 = 2
    u = 0 + 1 = 1

    Maka ∫ 2x² (x³ + 1)⁵ dx  {0...1}
    = 2/3 ∫ u⁵ du  { 1...2}
    = 2/3 [u⁶/6]  {1....2}
    = 1/9 [u⁶]  {2...1}
    = 1/9 [2⁶ - 1⁶]
    = 1/9 [64 - 1]
    = 63/9
    = 7