Pertanyaan

Nilai ∫ 1 36 x ( 3 + x ) 3/2 3 dx adalah...

Nilai $\int_{1}^{36} \frac{3}{x ( 3 + x ) ^{3/2}}$ dx adalah...

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Habis dalam

Klaim

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$integral subscript 1 superscript 36 fraction numerator 3 over denominator square root of x open parentheses 3 plus square root of x close parentheses to the power of 3 over 2 end exponent end fraction d x G u n a k a n space i n t e g r a l space s u b t i t u s i u equals 3 plus square root of x x equals 1 rightwards double arrow u equals 3 plus square root of 1 equals 4 x equals 36 rightwards double arrow u equals 3 plus square root of 36 equals 9 fraction numerator d u over denominator d x end fraction equals fraction numerator 1 over denominator 2 square root of x end fraction left right double arrow d x equals 2 square root of x space d u integral subscript 1 superscript 36 fraction numerator 3 over denominator square root of x open parentheses 3 plus square root of x close parentheses to the power of 3 over 2 end exponent end fraction d x equals integral subscript 4 superscript 9 fraction numerator 3 over denominator square root of x open parentheses u close parentheses to the power of 3 over 2 end exponent end fraction 2 square root of x d u integral subscript 4 superscript 9 6 u to the power of negative 3 over 2 end exponent d u 6. space open parentheses negative 2 close parentheses u to the power of negative 1 half end exponent open table row 9 row 4 end table close angle brackets minus 12 open parentheses 9 to the power of negative 1 half end exponent minus 4 to the power of negative 1 half end exponent close parentheses minus 12 open parentheses 1 third minus 1 half close parentheses minus 12 open parentheses negative 1 over 6 close parentheses equals 2$