Matematika

Pertanyaan

tollonggg donggg plisss
tollonggg donggg plisss

1 Jawaban

  • Gunakan prinsip integral, integral x^n dx = ((x/n+1)^(n+1)) + c

    1. integral 4x^3 = (4/(3+1))*x^(3+1) = (4/4)*(x^4) = x^4 + c
    2. integral 3x akar x
        pertama ubah dulu bentuk akar dalam bentuk pangkat
        = (3x)*x^1/2 = (3x)^(1+1/2) = 3x^3/2
        selanjutnya diintegralkan
        3/(3/2+1)*x^(3/2+1) = 3/(5/2)x^(5/2) = 6/5*(x^5/2) + c
    3. 1/(x^2) sama nilainya dengan x^-2
         integralkan x^-2 = x/(-2+1)^(-2+1) = (x/-1)^-1 = -x^-1 +c = -(1/x) + c
    4. 1/3x^4 sama nilainya dengan 3x^-4
         integralkan 3x^-4 = 3/(-4+1)*x^(-4+1) = 3/-3*x^-3 = -x^-3 + c = (-(1/x^3)) + c
    5. 1/4x*akar x sama nilainya dengan 1/(4*x^(1+1/2)) = 1/4*x^(3/2) = 4*x^(-3/2)
         integralkan 4x^(-3/2) = 4/(-3/2+1)*x^(-3/2+1) = 4/(-1/2)*x^(-1/2) = -8*x^(-1/2)
         = 1/(8x^1/2) = (1/ akar 8x) + c
    6. 2x^4 akar pangkat 5 dari x^2 dapat diubah menjadi 2x^4*x^2/5 = 2*x^22/5
        integralkan 2x^22/5 menjadi 2/(22/5+1)*x^(22/5+1) = 2/(27/5)*x^(27/5)
        = (10/27*x^27/5) + c