Pertanyaan

∫ 4 x 3 + 2 x 2 d x = …

$\int 4 x^{3} + 2 x^{2} d x = \dots$

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

hasil penyelesaiannya adalah .

hasil penyelesaiannya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 30 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent left parenthesis 3 x minus 1 right parenthesis plus C end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 30 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent left parenthesis 3 x minus 1 right parenthesis plus C end cell end table

Pembahasan

Diberikan bentuk aljabar seperti pada soal. Fungsi di dalamnya dapat disederhanakan seperti berikut : Dimisalkan : Dengan demikian, penyelesaian bentuk integral di atas adalah Jadi, hasil penyelesaiannya adalah .

Diberikan bentuk aljabar seperti pada soal. Fungsi di dalamnya dapat disederhanakan seperti berikut :

table attributes columnalign right center left columnspacing 0px end attributes row cell integral square root of 4 x cubed plus 2 x squared end root space d x end cell equals cell integral square root of x squared times open parentheses 4 x plus 2 close parentheses end root space d x end cell row blank equals cell integral x square root of 4 x plus 2 end root space d x end cell end table

Dimisalkan :

u equals x space rightwards arrow space d u equals d x

Dengan demikian, penyelesaian bentuk integral di atas adalah

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral x square root of 4 x plus 2 end root space d x end cell row blank equals cell u v minus integral v space d u end cell row blank equals cell x open parentheses 1 over 6 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent close parentheses minus 1 over 6 integral left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent space d x end cell row blank equals cell x over 6 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent minus 1 over 6 times 1 fourth times 2 over 5 left parenthesis 4 x plus 2 right parenthesis to the power of 5 over 2 end exponent plus C end cell row blank equals cell 1 over 6 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent open parentheses x minus 1 over 10 left parenthesis 4 x plus 2 right parenthesis close parentheses plus C end cell row blank equals cell 1 over 6 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent open parentheses fraction numerator 10 x minus 4 x minus 2 over denominator 10 end fraction close parentheses plus C end cell row blank equals cell 1 over 6 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent open parentheses fraction numerator 6 x minus 2 over denominator 10 end fraction close parentheses plus C end cell row blank equals cell 1 over 6 times 2 over 10 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent left parenthesis 3 x minus 1 right parenthesis plus C end cell row blank equals cell 1 over 30 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent left parenthesis 3 x minus 1 right parenthesis plus C end cell end table$

Jadi, hasil penyelesaiannya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 30 left parenthesis 4 x plus 2 right parenthesis to the power of 3 over 2 end exponent left parenthesis 3 x minus 1 right parenthesis plus C end cell end table .