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Diberikan . Jika G(0) = 0, maka G(1) adalah ...

Diberikan begin mathsize 14px style G open parentheses x close parentheses equals integral square root of x to the power of 4 plus 5 x end root left parenthesis 12 x cubed plus 15 right parenthesis blank d x end style. Jika G(0) = 0, maka G(1) adalah ...

  1. begin mathsize 14px style 4 square root of 6 end style

  2. begin mathsize 14px style 4 square root of 12 end style

  3. begin mathsize 14px style 6 square root of 6 end style

  4. begin mathsize 14px style 6 square root of 12 end style

  5. begin mathsize 14px style 12 square root of 6 end style

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Pembahasan

Misalkan . Didapat Sehingga kita dapatkan hasil sebagai berikut Maka G(x) dapat dituliskan ulang sebagai . Diketahui G(0) = 0, maka Sehingga . Maka

begin mathsize 14px style G open parentheses x close parentheses equals integral square root of x to the power of 4 plus 5 x end root left parenthesis 12 x cubed plus 15 right parenthesis blank d x end style

Misalkan begin mathsize 14px style u equals x to the power of 4 plus 5 x end style. Didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d u over denominator d x end fraction end cell equals cell 4 x cubed plus 53 end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell 12 x cubed plus 15 end cell row cell integral 3 blank open parentheses fraction numerator d u over denominator d x end fraction close parentheses d x end cell equals cell integral left parenthesis 12 blank x cubed plus 15 right parenthesis blank d x end cell row blank blank cell 3 integral open parentheses fraction numerator d u over denominator d x end fraction close parentheses d x equals integral left parenthesis 12 blank x cubed plus 15 right parenthesis blank d x end cell row blank blank cell 3 integral d u equals integral left parenthesis 12 blank x cubed plus 15 right parenthesis blank d x end cell end table end style

Sehingga kita dapatkan hasil sebagai berikut

begin mathsize 14px style integral square root of x to the power of 4 plus 5 x end root left parenthesis 12 x cubed plus 15 right parenthesis blank d x equals 3 integral square root of u blank d u equals 3 times open parentheses 2 over 3 close parentheses open parentheses u close parentheses to the power of 3 over 2 end exponent plus C equals 2 square root of u cubed end root plus C equals 2 times u square root of u plus C equals 2 left parenthesis x to the power of 4 plus 5 x right parenthesis square root of x to the power of 4 plus 5 x end root plus C end style

Maka G(x) dapat dituliskan ulang sebagai begin mathsize 14px style G open parentheses x close parentheses equals 2 left parenthesis x to the power of 4 plus 5 x right parenthesis square root of x to the power of 4 plus 5 x end root plus C end style. Diketahui G(0) = 0, maka

begin mathsize 14px style 0 equals 2 left parenthesis 0 to the power of 4 plus 5 times 0 right parenthesis square root of 0 to the power of 4 plus 5 times 0 end root plus C 0 equals 0 plus C 0 equals C end style

Sehingga begin mathsize 14px style G open parentheses x close parentheses equals 2 left parenthesis x to the power of 4 plus 5 x right parenthesis square root of x to the power of 4 plus 5 x end root end style.

Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell G open parentheses 1 close parentheses end cell equals cell 2 left parenthesis 1 to the power of 4 plus 5 times 1 right parenthesis square root of 1 to the power of 4 plus 5 times 1 end root end cell row blank equals cell 2 open parentheses 1 plus 5 close parentheses square root of 1 plus 5 end root end cell row blank equals cell 2 times 6 square root of 6 end cell row blank equals cell 12 square root of 6 end cell end table end style

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