RoboguruRoboguru
SD

Hasil dari ∫4x−x2​dx adalah...

Pertanyaan

Hasil dari integral square root of 4 x minus x squared end root d x adalah...

  1. 2 space a r c space sin open parentheses fraction numerator 2 plus x over denominator 2 end fraction close parentheses plus open parentheses fraction numerator 2 plus x over denominator 2 end fraction close parentheses square root of 4 x plus x squared end root plus C

  2. undefined

  3. undefined

  4. 2 space a r c space sin open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses minus open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses square root of 4 x minus x squared end root plus C

  5. 2 space a r c space sin open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses minus open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses square root of 4 x plus x squared end root plus C

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

misalkan:

x equals 2 space sin space u space plus 2 space rightwards double arrow u space equals space a r c space sin space open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses  d x equals 2 space cos space u space d u

perhatikan segitiga di bawah ini:

karena space sin space u space equals open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses sehingga diperoleh

cos space u space equals fraction numerator s a m p i n g over denominator m i r i n g end fraction equals fraction numerator square root of 2 squared minus left parenthesis x minus 2 right parenthesis squared end root over denominator 2 end fraction equals fraction numerator square root of 4 minus x squared plus 4 x minus 4 end root over denominator 2 end fraction equals fraction numerator square root of 4 x minus x squared end root over denominator 2 end fraction  sin space 2 u space equals space 2 space sin space u space cos space u space equals space 2 open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses open parentheses fraction numerator square root of 4 x minus x squared end root over denominator 2 end fraction close parentheses equals fraction numerator open parentheses x minus 2 close parentheses square root of 4 x minus x squared end root over denominator 2 end fraction  m a k a comma  integral subscript blank square root of 4 x minus x squared end root d x equals integral square root of x left parenthesis 4 minus x right parenthesis end root d x  equals integral square root of left parenthesis 2 space sin space u plus 2 right parenthesis left parenthesis 4 space minus space 2 space sin u minus 2 right parenthesis end root left parenthesis 2 space cos space u space d u right parenthesis  equals integral square root of open parentheses 2 plus 2 space sin space u close parentheses open parentheses 2 minus 2 space s i space u close parentheses end root left parenthesis 2 space cos space u space d u right parenthesis  equals integral square root of open parentheses 4 minus 4 space sin squared u close parentheses end root left parenthesis 2 space cos space u space d u right parenthesis  equals integral 2 square root of open parentheses 1 minus space sin squared u close parentheses end root open parentheses 2 space cos space u space d u close parentheses  equals 2 integral subscript blank square root of cos squared u end root left parenthesis 2 space cos space u space d u right parenthesis  equals 4 integral subscript blank cos space squared u space d u  equals 4 integral fraction numerator cos space 2 space u plus 1 over denominator 2 end fraction d u  equals 4 over 2 open parentheses 1 half sin space 2 u plus u close parentheses plus C  equals 4 over 2 open parentheses 1 half fraction numerator open parentheses x minus 2 close parentheses square root of 4 x minus x squared end root over denominator 2 end fraction a r c space sin open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses close parentheses plus C  equals fraction numerator open parentheses x minus 2 close parentheses over denominator 2 end fraction square root of 4 x minus x squared end root plus 2 space a r c space sin space open parentheses fraction numerator x minus 2 over denominator 2 end fraction close parentheses plus C

29

5.0 (1 rating)

Pertanyaan serupa

Hasil dari ∫16−9x2​dx=....

6

5.0

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

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia