Pertanyaan

∫ 1 2 ( 3 x 2 + 2 x − 4 ) d x = ...

$\int_{1}^{2} (3 x^{2} + 2 x - 4) d x$ = ...

N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Jawaban

hasil dari adalah .

hasil dari integral subscript 1 superscript 2 open parentheses 3 x squared plus 2 x minus 4 close parentheses straight d x

adalah

Pembahasan

Perhatikan perhitungan berikut ini. Ingat, integral: Maka: Jadi, hasil dari adalah .

Perhatikan perhitungan berikut ini.

Ingat, integral:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses d x end cell equals cell integral f open parentheses x close parentheses d x plus-or-minus integral g open parentheses x close parentheses d x end cell row cell integral x to the power of n d x end cell equals cell fraction numerator 1 over denominator 1 plus n end fraction x to the power of n plus 1 end exponent plus C end cell row cell integral c d x end cell equals cell c x plus C end cell end table$

Maka:

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

Jadi, hasil dari integral subscript 1 superscript 2 open parentheses 3 x squared plus 2 x minus 4 close parentheses straight d x adalah .