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Jika , maka nilai  adalah ....

Jika integral subscript 2 superscript 5 space f left parenthesis x right parenthesis d x equals square root of 2, maka nilai integral subscript 1 superscript 2 1 over x squared f open parentheses 1 plus 2 over x close parentheses space d x adalah ....

  1. fraction numerator square root of 2 over denominator 4 end fraction

  2. fraction numerator square root of 2 over denominator 2 end fraction

  3. square root of 2

  4. 2 square root of 2

  5. 4undefined

Jawaban:

integral from 1 to 2 of 1 over straight x squared straight f open parentheses 1 plus 2 over straight x close parentheses dx  Substitusi space straight y equals 1 plus 2 over straight x space maka  straight y equals 1 plus 2 straight x to the power of negative 1 end exponent  dy equals negative 2 straight x to the power of negative 2 end exponent straight space dx  dy equals negative 2 over straight x squared dx  box enclose negative 1 half straight space dy equals 1 over straight x squared straight space dx end enclose  Untuk space straight x equals 1 comma space maka space straight y equals 1 plus 2 over 1 equals 1 plus 2 equals box enclose 3  Untuk space straight x equals 2 comma space maka space straight y equals 1 plus 2 over 2 equals 1 plus 1 equals box enclose 2  Sehingga  integral from 1 to 2 of 1 over straight x squared straight f open parentheses 1 plus 2 over straight x close parentheses dx equals integral from 1 to 2 of straight f open parentheses 1 plus 2 over straight x close parentheses.1 over straight x squared dx equals integral from 3 to 2 of straight f open parentheses straight y close parentheses open parentheses negative 1 half straight space dy close parentheses equals negative 1 half integral from 3 to 2 of straight f open parentheses straight y close parentheses dy  equals 1 half integral from 2 to 3 of straight f open parentheses straight y close parentheses dy equals 1 half integral from 2 to 3 of straight f open parentheses straight x close parentheses dx equals box enclose fraction numerator square root of 2 over denominator 2 end fraction end enclose

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