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Selesaikan integral berikut! c.

Pertanyaan

Selesaikan integral berikut!

c. begin mathsize 14px style integral 2 fourth root of x cubed end root d x end style

  1. ...undefined 

  2. ...undefined 

Pembahasan Soal:

Perhatikan perhitungan berikut ini.

begin mathsize 14px style integral a x to the power of n d x equals a integral x to the power of n d x equals a open square brackets fraction numerator 1 over denominator n plus 1 end fraction x to the power of n plus 1 end exponent close square brackets plus C end style

Maka integral begin mathsize 14px style integral 2 fourth root of x cubed end root d x end style yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral 2 fourth root of x cubed end root d x end cell equals cell 2 integral fourth root of x cubed end root d x end cell row blank equals cell 2 integral x to the power of 3 over 4 end exponent d x end cell row blank equals cell 2 open parentheses fraction numerator 1 over denominator begin display style 3 over 4 plus 1 end style end fraction x to the power of 3 over 4 plus 1 end exponent close parentheses plus C end cell row blank equals cell 2 open parentheses fraction numerator 1 over denominator begin display style 7 over 4 end style end fraction x to the power of 7 over 4 end exponent close parentheses plus C end cell row blank equals cell 2 open parentheses 4 over 7 x to the power of 7 over 4 end exponent close parentheses plus C end cell row blank equals cell 8 over 7 x to the power of 7 over 4 end exponent plus C end cell row blank equals cell 8 over 7 fourth root of x to the power of 7 end root plus C end cell end table end style 

Jadi, nilai begin mathsize 14px style integral 2 fourth root of x cubed end root d x end style yaitu begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 8 over 7 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fourth root of x to the power of 7 end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table end style.

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Terakhir diupdate 20 Mei 2021

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