Pertanyaan

Hasil dari adalah ....

Hasil dari integral 1 half open parentheses x plus 1 close parentheses open parentheses 1 minus x close parentheses squared blank straight d x adalah ....

N. Putri

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan perhitungan berikut! Jika maka diperoleh hasil sebagai berikut. Jadi, jawaban yang tepat adalah B.

Perhatikan perhitungan berikut!

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral 1 half open parentheses x plus 1 close parentheses open parentheses 1 minus x close parentheses squared blank straight d x end cell row blank equals cell integral 1 half open parentheses x cubed minus x squared minus x plus 1 close parentheses blank straight d x end cell row blank equals cell 1 half integral open parentheses x cubed minus x squared minus x plus 1 close parentheses blank straight d x end cell row blank equals cell 1 half open parentheses integral x cubed blank straight d x minus integral x squared blank straight d x minus integral x blank straight d x plus integral 1 blank straight d x close parentheses end cell row blank equals cell 1 half open parentheses 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 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 minus 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 open parentheses x plus C subscript 4 close parentheses close parentheses end cell row blank equals cell 1 half open parentheses open parentheses 1 fourth x to the power of 4 plus C subscript 1 close parentheses minus open parentheses 1 third x cubed plus C subscript 2 close parentheses minus open parentheses 1 half x squared plus C subscript 3 close parentheses plus open parentheses x plus C subscript 4 close parentheses close parentheses end cell row blank equals cell 1 half open parentheses 1 fourth x to the power of 4 plus C subscript 1 minus 1 third x cubed minus C subscript 2 minus 1 half x squared minus C subscript 3 plus x plus C subscript 4 close parentheses end cell row blank equals cell 1 over 8 x to the power of 4 plus C subscript 1 over 2 minus 1 over 6 x cubed minus C subscript 2 over 2 minus 1 fourth x squared minus C subscript 3 over 2 plus x over 2 plus C subscript 4 over 2 end cell row blank equals cell 1 over 8 x to the power of 4 minus 1 over 6 x cubed minus 1 fourth x squared plus x over 2 plus C subscript 1 over 2 minus C subscript 2 over 2 minus C subscript 3 over 2 plus C subscript 4 over 2 end cell end table end style$

Jika begin mathsize 12px style C subscript 1 over 2 minus C subscript 2 over 2 minus C subscript 3 over 2 plus C subscript 4 over 2 equals C comma end style maka diperoleh hasil sebagai berikut.

Jadi, jawaban yang tepat adalah B.