Plo sha pove rhni plosha zadanoyi poverhni Grubo kazhuchi ye chislovoyu harakteristikoyu kilkosti poverhni Vimiryuyetsya v kvadratnih odinicyah dovzhini Obchislennya RedaguvatiYaksho poverhnyu parametrizovano tobto zadano vektornoyu funkciyeyu r u v displaystyle mathbf r u v todi plosha S S poverhni u v W displaystyle u v in Omega obchislyuyetsya za formuloyu 1 S W r u r v d u d v displaystyle S iint limits Omega r u times r v dudv de r u r u displaystyle r u frac partial r partial u ta r v r v displaystyle r v frac partial r partial v dotichni vektori r u r v displaystyle r u times r v vektornij dobutok dvoh vektoriv Inshij viglyad ploshi parametrichno zadanoyi poverhni S W E G F 2 d u d v displaystyle S iint limits Omega sqrt EG F 2 dudv de E F G displaystyle E F G koeficiyenti pershoyi kvadratichnoyi formi E r u r u G r v r v F r u r v displaystyle E left r u r u right G left r v r v right F left r u r v right Yaksho poverhnyu W Omega zadano funkciyeyu z z x y displaystyle z z x y nad deyakoyu oblastyu x y W displaystyle x y in Omega abo W displaystyle Omega ye proyekciyeyu poverhni W Omega na ploshinu x O y displaystyle xOy 2 todi S W d W W 1 z x 2 z y 2 d x d y displaystyle S iint limits Omega d Omega iint limits Omega sqrt 1 left frac partial z partial x right 2 left frac partial z partial y right 2 dxdy Posilannya Redaguvati Eric Weisstein CRC Concise Encylopedia of Mathematics Myshkis A D 1973 Lekcii po Vysshej Matematika Div takozh Redaguvati Portal Matematika Ob yem Paradoks malyara Plosha Poverhnevij integral Poverhnya obertannya Ce nezavershena stattya z matematiki Vi mozhete dopomogti proyektu vipravivshi abo dopisavshi yiyi Otrimano z https uk wikipedia org w index php title Plosha poverhni amp oldid 36303864
