Pertanyaan

Harga dari : ∫ 0 6 ( 3 x − 2 1 x 2 ) d x = ...

Harga dari :

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

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Habis dalam

Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

harga dari adalah .

harga dari integral subscript 0 superscript 6 open parentheses 3 x minus 1 half x squared close parentheses d x

adalah

Pembahasan

Integral memiliki aturan sebagai berikut, Maka, Jadi, harga dari adalah .

Integral memiliki aturan sebagai berikut,

$integral x to the power of n d x equals fraction numerator x to the power of n plus 1 end exponent over denominator n plus 1 end fraction$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript blank superscript blank open parentheses 3 x minus 1 half x squared close parentheses d x end cell equals cell 3 integral x d x minus 1 half integral x squared d x end cell row blank blank blank row cell integral x d x end cell equals cell fraction numerator x to the power of 1 plus 1 end exponent over denominator 1 plus 1 end fraction end cell row blank equals cell x squared over 2 end cell row blank blank blank row cell integral x squared d x end cell equals cell fraction numerator x to the power of 2 plus 1 end exponent over denominator 2 plus 1 end fraction end cell row blank equals cell x cubed over 3 end cell row cell 3 integral x d x minus 1 half integral x squared d x end cell equals cell 3 open parentheses x squared over 2 close parentheses minus 1 half open parentheses x cubed over 3 close parentheses end cell row blank equals cell fraction numerator 3 x squared over denominator 2 end fraction minus x cubed over 6 end cell row blank equals cell fraction numerator 9 x squared minus x cubed over denominator 6 end fraction end cell row blank equals cell fraction numerator x squared left parenthesis 9 minus x right parenthesis over denominator 6 end fraction plus C end cell row blank equals cell negative fraction numerator left parenthesis x minus 9 right parenthesis x squared over denominator 6 end fraction plus C end cell row cell integral subscript 0 superscript 6 open parentheses 3 x minus 1 half x squared close parentheses d x end cell equals cell negative fraction numerator left parenthesis 6 minus 9 right parenthesis 6 squared over denominator 6 end fraction minus open parentheses negative fraction numerator left parenthesis 0 minus 9 right parenthesis 0 squared over denominator 6 end fraction close parentheses end cell row blank equals cell negative fraction numerator left parenthesis negative 3 right parenthesis 36 over denominator 6 end fraction minus open parentheses 0 over 6 close parentheses end cell row blank equals cell 108 over 6 end cell row blank equals 18 row blank blank blank end table$

Jadi, harga dari integral subscript 0 superscript 6 open parentheses 3 x minus 1 half x squared close parentheses d x adalah .