Question

Bantu jawab pakai cara​

Answer 1

Verified answer

▪︎soal1:[tex]\int{(2x+5)^{-\frac{1}{2}}}dx =[/tex]

[tex](2x+5)^{\frac{1}{2}} + C = [/tex]

▪︎soal2:[tex]\int{(5x^2+1)(\sqrt(5x^3+3x-4))}dx = [/tex]

[tex]\frac{2}{9}(5x^3 + 3x - 4)^{\frac{3}{2}} + C [/tex]

[tex]\\\green{Diketahui:} [/tex]

▪︎soal1:[tex]\int{(2x+5)^{-\frac{1}{2}}}dx =[/tex]

▪︎soal2:[tex]\int{(5x^2+1)(\sqrt(5x^3+3x-4))}dx = [/tex]

[tex]\purple{Ditanya:}[/tex]

▪︎Hasil

[tex]\\\\\blue{Pembahasan:}\\[/tex]

memakai INTEGRAL SUBSTITUSI.

Dimisalkan suatu fungsi:

u = f(x)

lalu dicari du dan dx nya.

[tex]\\[/tex]

soal1:

u = f(x)

u = 2x + 5

du = 2 dx

dx = [tex]\frac{1}{2}[/tex]du

[tex]\\[/tex]

[tex]\int{(2x+5)^{-\frac{1}{2}}}dx =[/tex]

[tex]\int{(u)^{-\frac{1}{2}}}.\frac{1}{2}du =[/tex]

[tex]\frac{1}{2}\int{(u)^{-\frac{1}{2}}}du =[/tex]

[tex]\frac{1}{2}.\frac{1}{\frac{1}{2}}u^{\frac{1}{2}} =[/tex]

[tex]u^{\frac{1}{2}} = [/tex]

[tex](2x+5)^{\frac{1}{2}} + C [/tex]

[tex]\\[/tex]

soal2:

u = 5x³ + 3x - 4

du = (15x² +3)dx

du = 3(5x²+1)dx

[tex]\frac{1}{3}[/tex]du = (5x² + 1)dx

[tex]\\[/tex]

[tex]\int{(5x^2+1)(\sqrt(5x^3+3x-4))}dx = [/tex]

[tex]\int{\sqrt{u}.\frac{1}{3}du} = [/tex]

[tex]\frac{1}{3}\int{\sqrt{u}.du} = [/tex]

[tex]\frac{1}{3}.\frac{1}{\frac{3}{2}}u^{\frac{3}{2}} =[/tex]

[tex]\frac{2}{9}u^{\frac{3}{2}} =[/tex]

[tex]\frac{2}{9}(5x^3 + 3x - 4)^{\frac{3}{2}} + C [/tex]

[tex]\\\\\blue{Pelajari~lebih~ lanjut:}[/tex]

MATERI Soal integral:

•https://brainly.co.id/tugas/12392257

•https://brainly.co.id/tugas/13591083

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[tex]\\\\\blue{Detail~ Jawaban:}[/tex]

[tex]\bullet[/tex]Mapel : Matematika

[tex]\bullet[/tex] Kelas : 12

[tex]\bullet[/tex] Materi : Bab 1 Integral

[tex]\bullet[/tex] Kata Kunci : Integral substitusi

[tex]\bullet[/tex]Kode soal : 2

[tex]\bullet[/tex] Kode kategori : 12.2.1