Iklan

Iklan

Pertanyaan

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

Nilai adalah...

  1. 1

  2. 2

  3. 3

  4. 4

  5. 5

Iklan

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Iklan

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

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

2

Iklan

Iklan

Pertanyaan serupa

Nilai ∫ 0 3 ​ x + 1 ​ 3 x ​ d x adalah...

1

4.3

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia