Pertanyaan

Nilai a yang memenuhi ∫ a 1 12 x ( x 2 + 1 ) 2 d x = 14 adalah

Nilai a yang memenuhi

$\int_{a}^{1} 12 x (x^{2} + 1)^{2} d x = 14$ adalah

-2
-1
0
1

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Klaim

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Misalkan Maka

Misalkan

$u equals x squared plus 1 fraction numerator d u over denominator d x end fraction equals 2 x d x equals fraction numerator d u over denominator 2 x end fraction$

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript 1 12 x space left parenthesis x squared plus 1 right parenthesis squared space d x end cell equals 14 row cell integral subscript a superscript 1 up diagonal strike 12 x end strike space left parenthesis u right parenthesis squared space fraction numerator d u over denominator up diagonal strike 2 x end strike end fraction end cell equals 14 row cell integral subscript a superscript 1 space 6 left parenthesis u right parenthesis squared space d u end cell equals 14 row cell open square brackets 6 over 3 left parenthesis u right parenthesis cubed space close square brackets table row 1 row space row a end table end cell equals 14 row cell open square brackets 2 left parenthesis x squared plus 1 right parenthesis cubed close square brackets table row 1 row a end table end cell equals 14 row cell 2 left parenthesis 1 squared plus 1 right parenthesis cubed minus 2 left parenthesis a squared plus 1 right parenthesis cubed end cell equals 14 row cell 16 minus 2 left parenthesis a squared plus 1 right parenthesis cubed end cell equals 14 row cell left parenthesis a squared plus 1 right parenthesis cubed end cell equals 1 row cell a squared plus 1 end cell equals 1 row a equals 0 end table$