Pertanyaan

Hasil dari ∫ 0 2 3 ( x + 1 ) ( x − 6 ) d x = ...

Hasil dari $\int_{0}^{2} 3 (x + 1) (x - 6) d x = ...$

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

$integral subscript a superscript b a x to the power of n d x equals open square brackets fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent close square brackets subscript a superscript b equals open parentheses fraction numerator a over denominator n plus 1 end fraction b to the power of n plus 1 end exponent close parentheses minus open parentheses fraction numerator a over denominator n plus 1 end fraction a to the power of n plus 1 end exponent close parentheses integral subscript 0 superscript 2 3 left parenthesis x plus 1 right parenthesis left parenthesis x minus 6 right parenthesis d x equals integral subscript 0 superscript 2 3 left parenthesis x squared minus 5 x minus 6 right parenthesis d x equals integral subscript 0 superscript 2 left parenthesis 3 x squared minus 15 x minus 18 right parenthesis d x equals left square bracket x cubed minus 15 over 2 x squared minus 18 x right square bracket subscript 0 superscript 2 equals open parentheses left parenthesis 2 right parenthesis cubed minus 15 over 2 left parenthesis 2 right parenthesis squared minus 18 left parenthesis 2 right parenthesis close parentheses minus open parentheses left parenthesis 0 right parenthesis cubed minus 15 over 2 left parenthesis 0 right parenthesis squared minus 18 left parenthesis 0 right parenthesis close parentheses equals left parenthesis 8 minus 30 minus 36 right parenthesis minus left parenthesis 0 right parenthesis equals negative 58$