Tentukan antiturunan dari f(x) =  x21​

Pertanyaan

Tentukan antiturunan dari f italic left parenthesis x italic right parenthesis italic space italic equals italic space italic space x to the power of italic 1 over italic 2 end exponent

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pembahasan

begin mathsize 14px style F left parenthesis x right parenthesis equals x to the power of begin inline style 3 over 2 end style end exponent f apostrophe left parenthesis x right parenthesis equals 3 over 2 x to the power of begin inline style 1 half end style end exponent end style 

 Sehingga, antiturunan dari begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals 3 over 2 x to the power of begin inline style 1 half end style end exponent end style adalah begin mathsize 14px style F left parenthesis x right parenthesis equals x to the power of begin inline style 3 over 2 end style end exponent plus C end style 

Maka, antiturunan dari begin mathsize 14px style f left parenthesis x right parenthesis equals x to the power of begin inline style 1 half end style end exponent end style adalah

begin mathsize 14px style f left parenthesis x right parenthesis equals x to the power of begin inline style 1 half end style end exponent f left parenthesis x right parenthesis equals 2 over 3 left parenthesis 3 over 2 x to the power of begin inline style 1 half end style end exponent right parenthesis plus C F left parenthesis x right parenthesis equals 2 over 3 x to the power of begin inline style 3 over 2 end style end exponent plus C F left parenthesis x right parenthesis equals fraction numerator 2 x square root of x over denominator 3 end fraction plus C end style  

 

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