Pertanyaan

Tentukan hasil dari integral berikut: f. Tentukan hasil dari ∫ ( 18 x 2 − 12 x ) x 3 − x 2 + 2 d x .

Tentukan hasil dari integral berikut:

f. Tentukan hasil dari $\int (18 x^{2} - 12 x) x^{3} - x^{2} + 2 d x$ .

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

hasil integral fungsi di atas adalah .

hasil integral fungsi di atas adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x cubed minus x squared plus 2 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of x cubed minus x squared plus 2 end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table

Pembahasan

Dengan menggunakan metode subtitusi Sehingga Dengan demikian hasil integral fungsi di atas adalah .

Dengan menggunakan metode subtitusi

$table attributes columnalign right center left columnspacing 0px end attributes row U equals cell x cubed minus x squared plus 2 end cell row cell fraction numerator d U over denominator d x end fraction end cell equals cell 3 x squared minus 2 x end cell row cell d x end cell equals cell fraction numerator d U over denominator 3 x squared minus 2 x end fraction end cell end table$

Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral open parentheses 18 x squared minus 12 x close parentheses square root of x cubed minus x squared plus 2 end root space d x end cell row blank equals cell integral 6 open parentheses 3 x squared minus 2 x close parentheses square root of U fraction numerator d U over denominator 3 x squared minus 2 x end fraction end cell row blank equals cell integral 6 square root of U d U end cell row blank equals cell integral 6 U to the power of 1 half end exponent d U end cell row blank equals cell fraction numerator 6 over denominator begin display style 1 half end style plus 1 end fraction U to the power of 1 half plus 1 end exponent plus C end cell row blank equals cell fraction numerator 6 over denominator begin display style 3 over 2 end style end fraction U to the power of 3 over 2 end exponent plus C end cell row blank equals cell 6 cross times 2 over 3 U square root of U plus C end cell row blank equals cell 4 U square root of U plus C end cell row blank equals cell 4 open parentheses x cubed minus x squared plus 2 close parentheses square root of x cubed minus x squared plus 2 end root plus C end cell end table$

Dengan demikian hasil integral fungsi di atas adalah .