Pertanyaan

Jika ∫ 2 5 f ( x ) d x = 2 , maka nilai ∫ 1 2 x 2 1 f ( 1 + x 2 ) d x adalah ....

Jika $\int_{2}^{5} f (x) d x = 2$ , maka nilai $\int_{1}^{2} \frac{1}{x ^{2}} f (1 + \frac{2}{x}) d x$ adalah ....

$fraction numerator square root of 2 over denominator 4 end fraction$
$fraction numerator square root of 2 over denominator 2 end fraction$
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Klaim

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

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