Kalvar Kel 2
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![Page 1: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/1.jpg)
MASALAH ISOPERIMETRIK
![Page 2: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/2.jpg)
Awaluddin Fajar
Andre Kurniawan
Anggraeni Ayu S
Anis Yulia L
![Page 3: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/3.jpg)
Masalah Isoperimetrik
Minimumkan
Dengan dan dg kendala integral
dimana konstanta.
![Page 4: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/4.jpg)
Dengan menggunakan pengali Lagrange , Masalah Isoperimetrik merupakan suatu masalah untuk meminimumkan
![Page 5: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/5.jpg)
Jika merupakan solusi dari Masalah Isoperimetrik, maka solusi tersebut merupakan suatu fungsi yang meminimumkan
untuk konstanta tertentu.
Teorema 9
![Page 6: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/6.jpg)
PROBLEM
Carilah dengan fungsi yang kontinu terdiferensiabel di 0 sampai 1,
yang meminimumkan fungsional
dengan kendala
dengan syarat kendala
πΎ ( π¦ )=β«0
1
(π¦ 2 )ππ₯
![Page 7: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/7.jpg)
Penyelesaian
Diketahui
, maka
![Page 8: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/8.jpg)
diperoleh
![Page 9: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/9.jpg)
![Page 10: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/10.jpg)
dengan syarat kendala
dengan syarat kendala
![Page 11: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/11.jpg)
![Page 12: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/12.jpg)
![Page 13: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/13.jpg)
π¦ (π₯)=β30π π₯2ββ30π π₯=β30π π₯ (π₯β1 )
![Page 14: Kalvar Kel 2](https://reader034.fdokumen.com/reader034/viewer/2022051121/56d6bda91a28ab30168edbf0/html5/thumbnails/14.jpg)
TERIMA KASIH