Pertanyaan

Tentukan nilai dari ∫ 1 3 ( 2 x 2 − 3 x − 2 ) d x !

Tentukan nilai dari $\int_{1}^{3} (2 x^{2} - 3 x - 2) d x$ !

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari integral subscript 1 superscript 3 open parentheses 2 x squared minus 3 x minus 2 close parentheses d x

adalah

Pembahasan

Dengan demikian,nilai dari adalah .

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 1 superscript 3 open parentheses 2 x squared minus 3 x minus 2 close parentheses d x end cell row blank equals cell open square brackets fraction numerator 2 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 3 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus fraction numerator 2 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent close square brackets table row 3 row 1 end table end cell row blank equals cell open square brackets 2 over 3 x cubed minus 3 over 2 x squared minus 2 x close square brackets table row 3 row 1 end table end cell row blank equals cell open parentheses 2 over 3 open parentheses 3 close parentheses cubed minus 3 over 2 open parentheses 3 close parentheses squared minus 2 times 3 close parentheses minus open parentheses 2 over 3 open parentheses 1 close parentheses cubed minus 3 over 2 open parentheses 1 close parentheses squared minus 2 times 1 close parentheses end cell row blank equals cell open parentheses 2 over 3 times 27 minus 3 over 2 times 9 minus 6 close parentheses minus open parentheses 2 over 3 minus 3 over 2 minus 2 close parentheses end cell row blank equals cell open parentheses 108 over 6 minus 81 over 6 minus 36 over 6 close parentheses minus open parentheses 4 over 6 minus 9 over 6 minus 12 over 6 close parentheses end cell row blank equals cell negative 9 over 6 minus open parentheses negative 17 over 6 close parentheses end cell row blank equals cell fraction numerator negative 9 plus 17 over denominator 6 end fraction end cell row blank equals cell 8 over 6 end cell row blank equals cell 4 over 3 end cell end table$

Dengan demikian, nilai dari integral subscript 1 superscript 3 open parentheses 2 x squared minus 3 x minus 2 close parentheses d x adalah 4 over 3 .