Pertanyaan

Nilai ∫ 1 36 x ( 3 + x 2 3 3 d x adalah...

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

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Habis dalam

Klaim

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$i right parenthesis G u n a k a n space i n t e g r a l space s u b s t i t u s i integral from 1 to 36 of 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 S u b s t i t u s i space y equals 3 plus square root of x comma space m a k a y equals 3 plus x to the power of 1 half end exponent d y equals 1 half x to the power of negative 1 half end exponent space d x d y equals fraction numerator 1 over denominator 2 square root of x end fraction space d x 2 space d y equals fraction numerator 1 over denominator square root of x end fraction space d x 6 space d y equals fraction numerator 3 over denominator square root of x end fraction space d x U n t u k space x equals 1 comma space m a k a space y equals 3 plus square root of 1 equals 4. space U n t u k space x equals 36 comma space m a k a space y equals 3 plus square root of 36 equals 9. space space S e h i n g g a integral from 1 to 36 of 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 from 1 to 36 of 1 over open parentheses 3 plus square root of x close parentheses to the power of 3 over 2 end exponent bullet fraction numerator 3 over denominator square root of x end fraction d x equals integral from 4 to 9 of 1 over y to the power of 3 over 2 end exponent open parentheses 6 space d y close parentheses equals 6 integral from 4 to 9 of y to the power of negative 3 over 2 end exponent d y equals open fraction numerator 6 y to the power of negative 3 over 2 plus 1 end exponent over denominator negative 3 over 2 plus 1 end fraction close square brackets subscript 4 superscript 9 equals open fraction numerator 6 y to the power of negative 1 half end exponent over denominator negative 1 half end fraction close square brackets subscript 4 superscript 9 equals negative 12 open y to the power of negative 1 half end exponent close square brackets subscript 4 superscript 9 equals open negative fraction numerator 12 over denominator square root of y end fraction close square brackets subscript 4 superscript 9 equals negative fraction numerator 12 over denominator square root of 9 end fraction minus open parentheses negative fraction numerator 12 over denominator square root of 4 end fraction close parentheses equals negative 12 over 3 plus 12 over 2 equals negative 4 plus 6 equals 2$