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Консультация № 199927
20.12.2020, 12:55
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
┌
I = │(4y+6z)dx + (10x+14z)dy +(2x-4y)dz ,,
┘
AB
где AB - отрезок, соединяющий точки A(8,9,8) ; B(1,6,3) ,
пробегаемый от точки A к B .
┌
I = │(4y+6z)dx + (10x+14z)dy +(2x-4y)dz ,,
┘
AB
где AB - отрезок, соединяющий точки A(8,9,8) ; B(1,6,3) ,
пробегаемый от точки A к B .
Обсуждение
25.12.2020, 04:19
общий
это ответ
Здравствуйте, zhalykov.2015!
Это криволинейный интеграл второго рода, который в общем случае имеет вид
где AB - отрезок некоторой гладкой кривой, а функции P, Q, R непрерывны во всех точках этой кривой. Если кривая может быть задана параметрически в виде x = x(t), y = y(t), z = z(t), и при этом точкам A и B соответствуют значения параметра t[sub]A[/sub] и t[sub]B[/sub], то
В данном случае гладкая кривая представляет собой прямую, проходящую через точки A(8,9,8) и B(1,6,3), то есть имеющую направляющий вектор AB = {-7,-3,-5}. Следовательно, её параметрическим уравнением будет x = 8-7t, y = 9-3t, z = 8-5t, причём точкам A и B соответствуют t[sub]A[/sub] = 0 и t[sub]B[/sub] = 1. Тогда интеграл будет равен
Это криволинейный интеграл второго рода, который в общем случае имеет вид
где AB - отрезок некоторой гладкой кривой, а функции P, Q, R непрерывны во всех точках этой кривой. Если кривая может быть задана параметрически в виде x = x(t), y = y(t), z = z(t), и при этом точкам A и B соответствуют значения параметра t[sub]A[/sub] и t[sub]B[/sub], то
В данном случае гладкая кривая представляет собой прямую, проходящую через точки A(8,9,8) и B(1,6,3), то есть имеющую направляющий вектор AB = {-7,-3,-5}. Следовательно, её параметрическим уравнением будет x = 8-7t, y = 9-3t, z = 8-5t, причём точкам A и B соответствуют t[sub]A[/sub] = 0 и t[sub]B[/sub] = 1. Тогда интеграл будет равен
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