Pertanyaan

Hasil ∫ 1 4 ( 5 x − 2 x 1 ) d x adalah ...

Hasil $\int_{1}^{4} (5 x - \frac{1}{2 x}) d x$ adalah ...

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Habis dalam

Klaim

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Diperoleh hasil integral dengan batas atas dan batas bawah yaitu: Kemudian diperoleh nilai hasil integralnya yaitu: Maka, hasil adalah .

Diperoleh hasil integral dengan batas atas dan batas bawah yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 1 superscript 4 open parentheses 5 square root of x minus fraction numerator 1 over denominator 2 square root of x end fraction close parentheses d x end cell equals cell integral subscript 1 superscript 4 open parentheses 5 x to the power of 1 half end exponent minus fraction numerator 1 over denominator 2 x to the power of begin display style 1 half end style end exponent end fraction close parentheses d x end cell row blank equals cell right enclose fraction numerator 5 over denominator begin display style 1 half plus 1 end style end fraction x to the power of 1 half plus 1 end exponent minus x to the power of negative begin display style 1 half end style end exponent over 2 end enclose subscript space 1 end subscript superscript space 4 end superscript end cell row blank equals cell right enclose fraction numerator 5 over denominator begin display style 3 over 2 end style end fraction x to the power of 3 over 2 end exponent minus fraction numerator begin display style 1 half end style over denominator negative begin display style 1 half end style plus 1 end fraction x to the power of negative 1 half plus 1 end exponent end enclose subscript space 1 end subscript superscript space 4 end superscript end cell row blank equals cell right enclose 5 times 2 over 3 x to the power of 1 times x to the power of 1 half end exponent minus fraction numerator begin display style 1 half end style over denominator begin display style 1 half end style end fraction x to the power of negative 1 half plus 1 end exponent end enclose subscript space 1 end subscript superscript space 4 end superscript end cell row blank equals cell right enclose 10 over 3 x square root of x minus fraction numerator 1 over denominator down diagonal strike 2 end fraction times fraction numerator down diagonal strike 2 over denominator 1 end fraction x to the power of 1 half end exponent end enclose subscript space 1 end subscript superscript space 4 end superscript end cell row blank equals cell right enclose 10 over 3 x square root of x minus square root of x end enclose subscript space 1 end subscript superscript space 4 end superscript end cell end table$

Kemudian diperoleh nilai hasil integralnya yaitu:

Maka, hasil $integral subscript 1 superscript 4 open parentheses 5 square root of x minus fraction numerator 1 over denominator 2 square root of x end fraction close parentheses d x$ adalah 67 over 3 .