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Jika , maka nilai adalah...

Jika integral from 0 to 4 of f open parentheses x close parentheses d x equals square root of 2, maka nilai integral from 0 to 2 of x f open parentheses x squared close parentheses 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. 4 square root of 2

Jawaban:

integral from 0 to 2 of xf open parentheses straight x squared close parentheses dx  Substitusi space straight y equals straight x squared comma maka  dy equals 2 xdx  box enclose 1 half dy equals straight x straight space dx end enclose  Untuk space straight x equals 0 comma space maka space straight y equals 0 squared equals 0.  Untuk space straight x equals 2 comma space maka space straight y equals 2 squared equals 4.    Sehingga  integral from 0 to 2 of xf open parentheses straight x squared close parentheses dx equals integral from 0 to 2 of straight f open parentheses straight x squared close parentheses straight space straight x space dx equals integral from 0 to 4 of straight f open parentheses straight y close parentheses open parentheses 1 half dy close parentheses equals 1 half integral from 0 to 4 of straight f open parentheses straight y close parentheses dy  equals 1 half integral from 0 to 4 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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