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Консультация № 198132
03.04.2020, 15:47
0.00 руб.
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1
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Здравствуйте! Прошу помощи в следующем вопросе:
Преобразовать криволинейный интеграл вдвойной и вычислить его (по формуле Грина)
ϕС ydx+3xdy, где С: y=√(1-x^2 ), y=x, y=0
Преобразовать криволинейный интеграл вдвойной и вычислить его (по формуле Грина)
ϕС ydx+3xdy, где С: y=√(1-x^2 ), y=x, y=0
Обсуждение
08.04.2020, 05:55
общий
это ответ
Здравствуйте, fm11!
Для функций P(x,y) и Q(x,y), дифференцируемых на плоской области D, ограниченной замкнутым контуром C, формула Грина имеет вид
В данном случае P(x,y) = y, Q(x,y) = 3x и
Интеграл
численно равен площади области D, представляющей собой сектор круга радиуса 1, расположенный между прямыми y=x и y=0. Этот сектор, очевидно, составляет восьмую часть круга, то есть его площадь равна [$960$]R[sup]2[/sup]/8 = [$960$]/8. Следовательно,
Для функций P(x,y) и Q(x,y), дифференцируемых на плоской области D, ограниченной замкнутым контуром C, формула Грина имеет вид
В данном случае P(x,y) = y, Q(x,y) = 3x и
Интеграл
численно равен площади области D, представляющей собой сектор круга радиуса 1, расположенный между прямыми y=x и y=0. Этот сектор, очевидно, составляет восьмую часть круга, то есть его площадь равна [$960$]R[sup]2[/sup]/8 = [$960$]/8. Следовательно,
5
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