tollonggg donggg plisss
Matematika
charlotte10
Pertanyaan
tollonggg donggg plisss
1 Jawaban
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1. Jawaban deocms44
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