Pertanyaan

Hasil dari ∫ 3 x 3 x 2 + 1 d x adalah ...

Hasil dari $\int 3 x 3 x^{2} + 1 d x$ adalah ...

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan perhitungan berikut. Ingat, integral tak tentu: Misalkan: Maka: Jadi, hasil dari adalah . Dengan demikian, jawaban yang tepat adalah D.

Perhatikan perhitungan berikut.

Ingat, integral tak tentu:

$integral x to the power of n straight d x equals fraction numerator 1 over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C$

Misalkan:

$table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 3 x squared plus 1 end cell row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals cell 6 x end cell row cell straight d u end cell equals cell 6 x straight d x end cell row cell 1 half straight d u end cell equals cell 3 x straight d x end cell end table$

Maka:

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

Jadi, hasil dari integral 3 x square root of 3 x squared plus 1 end root straight d x adalah 1 third open parentheses 3 x squared plus 1 close parentheses square root of 3 x squared plus 1 end root plus C .

Dengan demikian, jawaban yang tepat adalah D.

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