Pertanyaan

Nilai dari ∫ − 1 1 ( 2 x 2 + 6 x − 1 ) d x = ... .

Nilai dari $\int_{- 1}^{1} (2 x^{2} + 6 x - 1) d x = ...$ .

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Gunakan konsep integral tertentu. Perhatikan perhitungan berikut. Jadi, jawaban yang tepat adalah D.

Gunakan konsep integral tertentu.

Perhatikan perhitungan berikut.

$begin mathsize 11px style table attributes columnalign right center left columnspacing 2px end attributes row cell integral subscript negative 1 end subscript superscript 1 open parentheses 2 x squared plus 6 x minus 1 close parentheses d x end cell equals cell open square brackets fraction numerator 2 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus fraction numerator 6 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus x close square brackets subscript negative 1 end subscript superscript 1 end cell row blank equals cell open square brackets 2 over 3 x cubed plus 3 x squared minus x close square brackets subscript negative 1 end subscript superscript 1 end cell row blank equals cell open square brackets 2 over 3 open parentheses 1 close parentheses cubed plus 3 open parentheses 1 close parentheses squared minus open parentheses 1 close parentheses close square brackets minus open square brackets 2 over 3 open parentheses negative 1 close parentheses cubed plus 3 open parentheses negative 1 close parentheses squared minus open parentheses negative 1 close parentheses close square brackets end cell row blank equals cell open square brackets 2 over 3 plus 3 minus 1 close square brackets minus open square brackets negative 2 over 3 plus 3 plus 1 close square brackets end cell row blank equals cell open square brackets 2 over 3 plus 2 close square brackets minus open square brackets negative 2 over 3 plus 4 close square brackets end cell row blank equals cell open square brackets fraction numerator 2 plus 6 over denominator 3 end fraction close square brackets minus open square brackets fraction numerator negative 2 plus 12 over denominator 3 end fraction close square brackets end cell row blank equals cell 8 over 3 minus 10 over 3 end cell row cell integral subscript negative 1 end subscript superscript 1 open parentheses 2 x squared plus 6 x minus 1 close parentheses d x end cell equals cell negative 2 over 3 end cell end table end style$

Jadi, jawaban yang tepat adalah D.