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Hasil dari integral 2 over 3 square root of x space d x adalah ....

  1. begin mathsize 14px style square root of x plus C end style

  2. begin mathsize 14px style x square root of x plus C end style

  3. begin mathsize 14px style 1 third x square root of x plus C end style

  4. begin mathsize 14px style 4 over 9 x square root of x plus C end style

  5. begin mathsize 14px style 9 over 4 x square root of x plus C end style

D. Natalia

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat kembali rumus integral fungsi aljabar berikut ini!

integral a x to the power of n space d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C comma space n not equal to negative 1

Akibatnya, didapat perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral 2 over 3 square root of x space d x end cell equals cell integral 2 over 3 x to the power of 1 half end exponent space d x end cell row blank equals cell fraction numerator begin display style 2 over 3 end style over denominator 1 half plus 1 end fraction x to the power of 1 half plus 1 end exponent plus C end cell row blank equals cell fraction numerator begin display style 2 over 3 end style over denominator 3 over 2 end fraction x to the power of 3 over 2 end exponent plus C end cell row blank equals cell 2 over 3 times 2 over 3 x to the power of 3 over 2 end exponent plus C end cell row blank equals cell 4 over 9 x to the power of 3 over 2 end exponent plus C end cell row blank equals cell 4 over 9 x to the power of 1 plus 1 half end exponent plus C end cell row blank equals cell 4 over 9 x times x to the power of 1 half end exponent plus C end cell row blank equals cell 4 over 9 x square root of x plus C end cell end table

Jadi, jawaban yang tepat adalah D.

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