Nilai  yang memenuhi persamaan ∫p3​(2x−1)dx=−6 adalah...

Pertanyaan

Nilai p yang memenuhi persamaan integral subscript p superscript 3 left parenthesis 2 x minus 1 right parenthesis d x equals negative 6 adalah...

  1. negative 2

  2. negative 3

  3. negative 1

  4. 2

  5. 1

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Konsep integral tentu:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b m x to the power of n d x end cell equals cell fraction numerator m over denominator n plus 1 end fraction x to the power of n plus 1 end exponent large right square bracket subscript space a end subscript superscript space b end superscript end cell row cell integral subscript a superscript b m x to the power of n d x end cell equals cell fraction numerator m over denominator n plus 1 end fraction b to the power of n plus 1 end exponent minus fraction numerator m over denominator n plus 1 end fraction a to the power of n plus 1 end exponent comma space dengan space n not equal to negative 1 end cell end table

Pembahasan:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript p superscript 3 left parenthesis 2 x minus 1 right parenthesis d x end cell equals cell negative 6 end cell row cell fraction numerator 2 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus x space large right square bracket subscript space p end subscript superscript space 3 end superscript end cell equals cell negative 6 end cell row cell 2 over 2 x squared minus x large right square bracket subscript space p end subscript superscript space 3 end superscript end cell equals cell negative 6 end cell row cell x squared minus x large right square bracket subscript space p end subscript superscript space 3 end superscript end cell equals cell negative 6 end cell row cell left parenthesis 3 squared minus 3 right parenthesis minus open parentheses p squared minus p close parentheses end cell equals cell negative 6 end cell row cell left parenthesis 9 minus 3 right parenthesis minus open parentheses p squared minus p close parentheses end cell equals cell negative 6 end cell row cell 6 minus p squared plus p end cell equals cell negative 6 end cell row cell negative p squared plus p end cell equals cell negative 6 minus 6 end cell row cell negative p squared plus p end cell equals cell negative 12 end cell row cell p squared minus p end cell equals 12 row cell p squared minus p minus 12 end cell equals 0 row cell open parentheses p minus 3 close parentheses open parentheses p plus 2 close parentheses end cell equals 0 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis p minus 3 right parenthesis end cell equals 0 row p equals cell 3 space end cell end table  atau  table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses p plus 2 close parentheses end cell equals 0 row p equals cell negative 2 end cell end table

Jadi, nilai p yang memenuhi adalah 3 atau negative 2.

Oleh karena itu, jawaban yang benar adalah A.

29

0.0 (0 rating)

Pertanyaan serupa

Jika f(x)=ax+b, ∫02​f(x)dx=4 dan ∫24​f(x)dx=6, maka selisih a dan b adalah ....

77

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