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Tentukan nilai integral dari ∫ x – 2 1 ​ ( x 3 + 3 ) d x

Tentukan nilai integral dari 

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G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

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Pembahasan

Rumus integral, Maka, Jadi,nilai integral dari adalah ,

Rumus integral,

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

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell integral x – 1 half left parenthesis x cubed plus 3 right parenthesis space d x end cell equals cell integral x minus fraction numerator x cubed plus 3 over denominator 2 end fraction end cell row blank equals cell integral x minus x cubed over 2 plus 3 over 2 end cell row blank equals cell negative 1 half integral x cubed d x plus integral x d x minus 3 over 2 integral 1 d x end cell row blank blank blank row cell integral x cubed d x end cell equals cell fraction numerator x to the power of 3 plus 1 end exponent over denominator 3 plus 1 end fraction end cell row blank equals cell x to the power of 4 over 4 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 1 d x end cell equals cell fraction numerator 1 x to the power of 0 plus 1 end exponent over denominator 0 plus 1 end fraction end cell row blank equals cell fraction numerator 1 x to the power of 1 over denominator 1 end fraction end cell row blank equals x row blank blank blank row cell negative 1 half integral x cubed d x plus integral x d x minus 3 over 2 integral 1 d x end cell equals cell negative 1 half open parentheses x to the power of 4 over 4 close parentheses plus x squared over 2 minus 3 over 2 open parentheses x close parentheses end cell row blank equals cell negative x to the power of 4 over 8 plus x squared over 2 minus fraction numerator 3 x over denominator 2 end fraction plus C end cell row blank equals cell fraction numerator negative x to the power of 4 plus 4 x squared minus 12 x over denominator 8 end fraction plus C end cell row blank equals cell negative fraction numerator x left parenthesis x cubed minus 4 x plus 12 right parenthesis over denominator 8 end fraction plus C end cell row blank blank blank end table

Jadi, nilai integral dari integral x – 1 half left parenthesis x cubed plus 3 right parenthesis space d x adalah negative fraction numerator x left parenthesis x cubed minus 4 x plus 12 right parenthesis over denominator 8 end fraction plus C,

 

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