Mavzu: Ikki karrali integral va uning tadbiqlari. Kurs ishi mavzu: Ikki karrali integral va uning tadbiqlari. Reja: I. Kirish. II. Asosiy qism

Yechish:






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11-misol. Qutb koordinatalar sistemasiga o‘tib chegaralangan soha yuzini toping.



Yechish:









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12-misol. aylanma paraboloid, silindr va tekisliklar bilan chegaralangan jismning hajmini toping.
Yechish:

D soha quyidagicha bo‘ladi:



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13-misol. Chegaralangan hajm yuzini toping.

Yechish:





14-misol. Chegaralangan hajm yuzini toping.

Yechish:

15-misol. Qutb koordinatalar sistemasiga o‘tib chegaralangan hajm yuzini toping.



Yechish:






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16-misol. Qutb koordinatalar sistemasiga o‘tib chegaralangan hajm yuzini toping.



Yechish:








17-misol. tekislikning silindir ichidagi qismini yuzini toping.
Yechish:







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18-misol. Chegaralangan sirt yuzasini toping.
chegaralangan sirt yuzasini toping.