Pertanyaan

Hasil dari

Hasil dari $integral from 1 to 2 of square root of x plus 1 over x end root open parentheses fraction numerator x squared minus 1 over denominator x squared end fraction close parentheses straight d x equals horizontal ellipsis$

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M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

dapat disimpulkan bahwa hasil dari adalah .

dapat disimpulkan bahwa hasil dari $integral from 1 to 2 of square root of x plus 1 over x end root open parentheses fraction numerator x squared minus 1 over denominator x squared end fraction close parentheses straight d x$ adalah 5 over 3 square root of 5 over 2 end root minus 4 over 3 square root of 2

5 over 3 square root of 5 over 2 end root minus 4 over 3 square root of 2

Pembahasan

Ingat cara untuk menentukan hasil dari suatu integral fungsi dengan bentuk fungsi seperti di atas dapat menggunakan metode inetgral parsial sebagai berikut. Misalkan Kemudian menentukan batas-batas baru Sehingga akan diperoleh Jadi, dapat disimpulkan bahwa hasil dari adalah .

Ingat cara untuk menentukan hasil dari suatu integral fungsi dengan bentuk fungsi seperti di atas dapat menggunakan metode inetgral parsial sebagai berikut.

Misalkan

Kemudian menentukan batas-batas baru

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 1 rightwards arrow u equals blank x plus 1 over x end cell row blank blank cell equals blank 1 plus 1 over 1 equals blank 1 plus 1 equals blank 2 end cell row blank blank blank end table

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 2 rightwards arrow u equals blank x plus 1 over x end cell row blank blank cell equals blank 2 plus 1 half equals blank 4 over 2 plus 1 half equals blank 5 over 2 end cell end table

Sehingga akan diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral from 1 to 2 of square root of x plus 1 over x end root open parentheses fraction numerator x squared minus 1 over denominator x squared end fraction close parentheses straight d x end cell equals cell integral from 1 to 2 of square root of x plus 1 over x end root open parentheses x squared over x squared minus 1 over x squared close parentheses straight d x end cell row blank equals cell integral from 1 to 2 of square root of x plus 1 over x end root open parentheses 1 minus 1 over x squared close parentheses straight d x end cell row blank equals cell integral from 1 to 2 of open parentheses x plus 1 over x close parentheses to the power of 1 half end exponent open parentheses 1 minus 1 over x squared close parentheses straight d x end cell row blank equals cell integral from 2 to 5 over 2 of u to the power of 1 half end exponent straight d u end cell row blank equals cell open square brackets fraction numerator 1 over denominator 1 half plus 1 end fraction u to the power of 1 half plus 1 end exponent close square brackets subscript 2 superscript 5 over 2 end superscript end cell row blank equals cell open square brackets fraction numerator 1 over denominator 1 half plus 2 over 2 end fraction u to the power of 1 half plus 2 over 2 end exponent close square brackets subscript 2 superscript 5 over 2 end superscript end cell row blank equals cell open square brackets fraction numerator 1 over denominator 3 over 2 end fraction u to the power of 3 over 2 end exponent close square brackets subscript 2 superscript 5 over 2 end superscript end cell row blank equals cell 2 over 3 open square brackets u to the power of 3 over 2 end exponent close square brackets subscript 2 superscript 5 over 2 end superscript end cell row blank equals cell 2 over 3 open square brackets open parentheses 5 over 2 close parentheses to the power of 3 over 2 end exponent minus 2 to the power of 3 over 2 end exponent close square brackets end cell row blank equals cell 2 over 3 open square brackets square root of open parentheses 5 over 2 close parentheses cubed end root minus square root of 2 cubed end root close square brackets end cell row blank equals cell 2 over 3 open square brackets square root of 125 over 8 end root minus square root of 8 close square brackets end cell row blank equals cell 2 over 3 open square brackets square root of 125 over 8 end root minus square root of 8 close square brackets end cell row blank equals cell 2 over 3 open square brackets square root of fraction numerator 25 cross times 5 over denominator 4 cross times 2 end fraction end root minus square root of 4 cross times 2 end root close square brackets end cell row blank equals cell 2 over 3 open square brackets 5 over 2 square root of 5 over 2 end root minus 2 square root of 2 close square brackets end cell row blank equals cell 10 over 6 square root of 5 over 2 end root minus 4 over 3 square root of 2 end cell row blank equals cell 5 over 3 square root of 5 over 2 end root minus 4 over 3 square root of 2 end cell end table$

Jadi, dapat disimpulkan bahwa hasil dari $integral from 1 to 2 of square root of x plus 1 over x end root open parentheses fraction numerator x squared minus 1 over denominator x squared end fraction close parentheses straight d x$ adalah 5 over 3 square root of 5 over 2 end root minus 4 over 3 square root of 2 .