Pertanyaan

∫ 1 p x 4 x 2 + 1 d x = 24 19 maka nilai adalah ...

$\int_{1}^{p} \frac{x ^{2} + 1}{x ^{4}} d x = \frac{19}{24}$ maka nilai $p$ adalah ...

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

nilai yang memenuhi adalah .

nilai

yang memenuhi adalah p equals 2

Pembahasan

Pada persamaan , uji nilai Jadi, nilai yang memenuhi adalah .

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 1 superscript p fraction numerator x squared plus 1 over denominator x to the power of 4 end fraction d x end cell equals cell 19 over 24 end cell row cell integral subscript 1 superscript p open parentheses x squared over x to the power of 4 plus 1 over x to the power of 4 close parentheses d x end cell equals cell 19 over 24 end cell row cell integral subscript 1 superscript p open parentheses x to the power of negative 2 end exponent plus x to the power of negative 4 end exponent close parentheses d x end cell equals cell 19 over 24 end cell row cell open square brackets fraction numerator 1 over denominator negative 1 end fraction x to the power of negative 1 end exponent plus fraction numerator 1 over denominator negative 3 end fraction x to the power of negative 3 end exponent close square brackets subscript 1 superscript p end cell equals cell 19 over 24 end cell row cell open square brackets negative x to the power of negative 1 end exponent minus 1 third x to the power of negative 3 end exponent close square brackets subscript 1 superscript p end cell equals cell 19 over 24 end cell row cell open square brackets negative 1 over x minus fraction numerator 1 over denominator 3 x cubed end fraction close square brackets subscript 1 superscript p end cell equals cell 19 over 24 end cell row cell open parentheses negative 1 over p minus fraction numerator 1 over denominator 3 p cubed end fraction close parentheses minus open parentheses negative 1 over 1 minus fraction numerator 1 over denominator 3 open parentheses 1 close parentheses cubed end fraction close parentheses end cell equals cell 19 over 24 end cell row cell open parentheses negative 1 over p minus fraction numerator 1 over denominator 3 p cubed end fraction close parentheses minus open parentheses negative 1 minus 1 third close parentheses end cell equals cell 19 over 24 end cell row cell open parentheses negative 1 over p minus fraction numerator 1 over denominator 3 p cubed end fraction close parentheses minus open parentheses negative 4 over 3 close parentheses end cell equals cell 19 over 24 end cell row cell open parentheses negative 1 over p minus fraction numerator 1 over denominator 3 p cubed end fraction close parentheses plus 4 over 3 end cell equals cell 19 over 24 end cell row cell open parentheses negative 1 over p minus fraction numerator 1 over denominator 3 p cubed end fraction close parentheses end cell equals cell 19 over 24 minus 4 over 3 end cell row cell open parentheses negative 1 over p minus fraction numerator 1 over denominator 3 p cubed end fraction close parentheses end cell equals cell fraction numerator 19 minus 32 over denominator 24 end fraction end cell row cell open parentheses negative 1 over p minus fraction numerator 1 over denominator 3 p cubed end fraction close parentheses end cell equals cell negative 13 over 24 end cell row cell 1 over p plus fraction numerator 1 over denominator 3 p cubed end fraction end cell equals cell 13 over 24 end cell row cell fraction numerator 24 p squared over denominator 24 p cubed end fraction plus fraction numerator 8 over denominator 24 p cubed end fraction end cell equals cell fraction numerator 13 p cubed over denominator 24 p cubed end fraction end cell row cell 24 p squared plus 8 end cell equals cell 13 p cubed end cell row cell 13 p cubed minus 24 p squared minus 8 end cell equals 0 end table$

Pada persamaan 13 p cubed minus 24 p squared minus 8 equals 0 , uji nilai p equals 2

table attributes columnalign right center left columnspacing 0px end attributes row cell 13 straight p cubed minus 24 straight p squared minus 8 end cell equals 0 row cell 13 open parentheses 2 close parentheses cubed minus 24 open parentheses 2 close parentheses squared minus 8 end cell equals 0 row cell 104 minus 96 minus 8 end cell equals 0 row 0 equals 0 row blank blank memenuhi end table

Jadi, nilai yang memenuhi adalah p equals 2 .