Jika ∫25f(x)dx=2, maka nilai ∫12x21f(1+x2)dx adalah ....

Pertanyaan

Jika $\int_2^5\;f(x)dx=\sqrt2$ , maka nilai $\int_1^2\frac1{x^2}f\left(1+\frac2x\right)\;dx$ adalah ....

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

Pembahasan:

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

Jawaban terverifikasi

Dijawab oleh:

N. Dwi

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Terakhir diupdate 05 Oktober 2021