Roboguru

integral subscript 0 superscript 4 3 x squared plus 2 sin squared invisible function application pi x blank d x equals horizontal ellipsis

Jawaban:

Ingat integral pada penjumlahan 2 fungsi dan ingat juga identitas pada trigonometri.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 x end cell equals cell cos squared space x minus sin squared space x end cell row cell cos space 2 x plus sin squared space x end cell equals cell cos squared space x end cell end table

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell cos squared space x plus sin squared space x end cell equals 1 row cell cos squared space x end cell equals cell 1 minus sin squared space x end cell end table

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell cos squared space x end cell equals cell 1 minus sin squared space x end cell row cell cos space 2 x plus sin squared space x end cell equals cell 1 minus sin squared space x end cell row cell cos space 2 x end cell equals cell 1 minus sin squared space x minus sin squared space x end cell row cell cos space 2 x end cell equals cell 1 minus 2 sin squared space x end cell row cell 2 sin squared space x end cell equals cell 1 minus cos space 2 x end cell end table

Maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 0 superscript 4 3 x squared plus 2 sin squared pi x blank d x end cell equals cell integral subscript 0 superscript 4 3 x squared blank d x plus integral subscript 0 superscript 4 2 sin squared pi x d x end cell row blank equals cell open square brackets 3 over 3 x cubed close square brackets subscript 0 superscript 4 plus integral subscript 0 superscript 4 1 minus cos space 2 x d x end cell row blank equals cell open square brackets x cubed close square brackets subscript 0 superscript 4 plus open square brackets x minus fraction numerator 1 over denominator 2 pi end fraction sin space 2 pi x close square brackets subscript 0 superscript 4 end cell row blank equals cell open square brackets 4 cubed minus 0 cubed close square brackets plus open square brackets open parentheses 4 minus fraction numerator 1 over denominator 2 pi end fraction sin space 2 pi times 4 close parentheses minus open parentheses 0 minus fraction numerator 1 over denominator 2 pi end fraction sin space 2 pi times 0 close parentheses close square brackets end cell row blank equals cell open square brackets 64 minus 0 close square brackets plus open square brackets open parentheses 4 minus fraction numerator 1 over denominator 2 pi end fraction sin space 8 pi close parentheses minus open parentheses 0 minus fraction numerator 1 over denominator 2 pi end fraction sin space 0 degree close parentheses close square brackets end cell row blank equals cell 64 plus open square brackets open parentheses 4 minus fraction numerator 1 over denominator 2 pi end fraction sin space 0 degree close parentheses minus open parentheses 0 minus fraction numerator 1 over denominator 2 pi end fraction sin space 0 degree close parentheses close square brackets end cell row blank equals cell 64 plus open square brackets open parentheses 4 minus fraction numerator 1 over denominator 2 pi end fraction times 0 close parentheses minus open parentheses 0 minus fraction numerator 1 over denominator 2 pi end fraction times 0 close parentheses close square brackets end cell row blank equals cell 64 plus open square brackets open parentheses 4 minus 0 close parentheses minus open parentheses 0 minus 0 close parentheses close square brackets end cell row blank equals cell 64 plus open square brackets 4 minus 0 close square brackets end cell row blank equals cell 64 plus 4 end cell row blank equals 68 end table

Jadi, dapat disimpulkan bahwa hasil dari integral subscript 0 superscript 4 3 x squared plus 2 sin squared pi x blank d x adalah 68.

0

Ruangguru

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved