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Консультация № 187365
24.05.2013, 09:53
87.71 руб.
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Обсуждение
24.05.2013, 14:27
общий
это ответ
Здравствуйте, Илья!
Из первого соотношения находим уравнение поверхности в явном виде
z=[$8730$](1-x2)
На плоскости z=0 имеем область, ограниченную кривыми x2=1 (т.е. x=1), 2x+y=2 (т.е. y=2-2x) и y=2.
Они ограничивают область G={0[$8804$]x[$8804$]1,2-2x[$8804$]y[$8804$]2}.
Элемент площади поверхности
dS=[$8730$](1+zx2+zy2)dxdy=dxdy/[$8730$](1-x2)
Искомая площадь равна интегралу по G от dS, т.е.
S=[$8747$]01(dx/[$8730$](1-x2))[$8747$]2-2x2dy=
=[$8747$]012xdx/[$8730$](1-x2)=-2[$8730$](1-x2)|01=2
Из первого соотношения находим уравнение поверхности в явном виде
z=[$8730$](1-x2)
На плоскости z=0 имеем область, ограниченную кривыми x2=1 (т.е. x=1), 2x+y=2 (т.е. y=2-2x) и y=2.
Они ограничивают область G={0[$8804$]x[$8804$]1,2-2x[$8804$]y[$8804$]2}.
Элемент площади поверхности
dS=[$8730$](1+zx2+zy2)dxdy=dxdy/[$8730$](1-x2)
Искомая площадь равна интегралу по G от dS, т.е.
S=[$8747$]01(dx/[$8730$](1-x2))[$8747$]2-2x2dy=
=[$8747$]012xdx/[$8730$](1-x2)=-2[$8730$](1-x2)|01=2
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