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Pertanyaan

Hasil dari integral x squared open parentheses 2 minus x cubed close parentheses to the power of 1 half end exponent d x equals...  

Pembahasan Soal:

Integral tersebut dapat diselesaikan dengan metode integral substitusi biasa berikut ini

Misalnya 

u equals 2 minus x cubed 

Maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d u over denominator d x end fraction end cell equals cell negative 3 x squared end cell row cell d x end cell equals cell negative fraction numerator d u over denominator 3 x squared end fraction end cell end table 

Sehingga 

 table attributes columnalign right center left columnspacing 0px end attributes row cell integral x squared open parentheses 2 minus x cubed close parentheses to the power of 1 half end exponent d x end cell equals cell integral x squared open parentheses u close parentheses to the power of 1 half end exponent open parentheses negative fraction numerator d u over denominator 3 x squared end fraction close parentheses end cell row blank equals cell negative 1 third integral u to the power of 1 half end exponent d u end cell row blank equals cell negative 1 third open parentheses fraction numerator 1 over denominator begin display style 3 over 2 end style end fraction u to the power of 3 over 2 end exponent close parentheses plus C end cell row blank equals cell negative 2 over 9 u to the power of 3 over 2 end exponent plus C end cell row blank equals cell negative 2 over 9 open parentheses 2 minus x cubed close parentheses to the power of 3 over 2 end exponent plus C end cell end table 

Dengan demikian, integral x squared open parentheses 2 minus x cubed close parentheses to the power of 1 half end exponent d x equals negative 2 over 9 open parentheses 2 minus x cubed close parentheses to the power of 3 over 2 end exponent plus C

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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