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Hasil dari adalah ....

Hasil dari integral open parentheses 2 minus x close parentheses squared open parentheses 3 x plus 1 close parentheses space d x adalah ....

  1. begin mathsize 14px style 3 over 4 x to the power of 4 minus 11 over 3 x cubed plus 4 x squared plus 4 x plus C end style

  2. begin mathsize 14px style 3 over 4 x to the power of 4 minus 11 over 3 x cubed minus 4 x squared plus 4 x plus C end style

  3. begin mathsize 14px style 3 over 4 x to the power of 4 minus 11 over 3 x cubed plus 4 x squared minus 4 x plus C end style

  4. begin mathsize 14px style 3 over 4 x to the power of 4 minus 11 over 3 x cubed plus 2 x squared plus 4 x plus C end style

  5. begin mathsize 14px style 3 over 4 x to the power of 4 minus 11 over 3 x cubed plus x squared plus 4 x plus C end style

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

jawaban yang tepat adalah A.

Pembahasan

Untuk menentukan hasil integral dari , perhatikan perhitungan berikut. Misalkan ,maka didapat hasil perhitungan sebagai berikut. Jadi, jawaban yang tepat adalah A.

Untuk menentukan hasil integral dari integral open parentheses 2 minus x close parentheses squared open parentheses 3 x plus 1 close parentheses space d x, perhatikan perhitungan berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral open parentheses 2 minus x close parentheses squared open parentheses 3 x plus 1 close parentheses space d x end cell row blank equals cell integral open parentheses 3 x cubed minus 11 x squared plus 8 x plus 4 close parentheses blank d x end cell row blank equals cell integral 3 x cubed blank d x minus integral 11 x squared blank d x plus integral 8 x blank d x plus integral 4 blank d x end cell row blank equals cell 3 open parentheses fraction numerator 1 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent plus C subscript 1 close parentheses minus 11 open parentheses fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus C subscript 2 close parentheses plus end cell row blank blank cell 8 open parentheses fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus C subscript 3 close parentheses plus 4 open parentheses x plus C subscript 4 close parentheses end cell row blank equals cell 3 open parentheses 1 fourth x to the power of 4 plus C subscript 1 close parentheses minus 11 open parentheses 1 third x cubed plus C subscript 2 close parentheses plus end cell row blank blank cell 8 open parentheses 1 half x squared plus C subscript 3 close parentheses plus 4 open parentheses x plus C subscript 4 close parentheses end cell row blank equals cell 3 over 4 x to the power of 4 plus 3 C subscript 1 minus 11 over 3 x cubed minus 11 C subscript 2 plus 4 x squared plus 8 C subscript 3 plus 4 x plus 4 C subscript 4 end cell row blank equals cell 3 over 4 x to the power of 4 minus 11 over 3 x cubed plus 4 x squared plus 4 x plus 3 C subscript 1 minus 11 C subscript 2 plus 8 C subscript 3 plus 4 C subscript 4 end cell end table end style

Misalkan 3 C subscript 1 minus 11 C subscript 2 plus 8 C subscript 3 plus 4 C subscript 4 equals C, maka didapat hasil perhitungan sebagai berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over 4 x to the power of 4 minus 11 over 3 x cubed plus 4 x squared plus 4 x plus 3 C subscript 1 minus 11 C subscript 2 plus 8 C subscript 3 plus 4 C subscript 4 end cell row blank equals cell 3 over 4 x to the power of 4 minus 11 over 3 x cubed plus 4 x squared plus 4 x plus C end cell end table end style

Jadi, jawaban yang tepat adalah A.

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