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Консультация № 182965
26.04.2011, 22:27
48.40 руб.
27.04.2011, 00:18
0
4
2
Здравствуйте! Прошу помощи в следующем вопросе:
Найти площадь S фигуры, ограниченной графиком функции в полярной системе координат:
[$961$]= cos (17[$966$])
Найти площадь S фигуры, ограниченной графиком функции в полярной системе координат:
[$961$]= cos (17[$966$])
Обсуждение
27.04.2011, 00:09
общий
это ответ
Здравствуйте, John_the_Revelator!
Площадь фигуры, ограниченной графиком функции в полярной системе координат вычисляется по формуле:
У нас [tnr][$961$]([$966$]) = cos(17[$966$])[/tnr], пределы интегрирования: a = 0, b = 2[tnr][$960$][/tnr].
Но, из=за того, что на половине участка [$961$] будет отрицательной величиной, значение интеграла необходимо поделить пополам
Тогда имеем:
Площадь фигуры, ограниченной графиком функции в полярной системе координат вычисляется по формуле:
У нас [tnr][$961$]([$966$]) = cos(17[$966$])[/tnr], пределы интегрирования: a = 0, b = 2[tnr][$960$][/tnr].
Но, из=за того, что на половине участка [$961$] будет отрицательной величиной, значение интеграла необходимо поделить пополам
Тогда имеем:
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
27.04.2011, 10:21
общий
это ответ
Здравствуйте, John_the_Revelator!
Предыдущий ответ требует исправления. При изменении полярного угла в пределах 2*pi на половине длины этого участка величина [$961$] будет отрицательна. Поэтому полученный ответ нужно уменьшить в два раза:
Ответ: S=Pi/4.
Предыдущий ответ требует исправления. При изменении полярного угла в пределах 2*pi на половине длины этого участка величина [$961$] будет отрицательна. Поэтому полученный ответ нужно уменьшить в два раза:
Ответ: S=Pi/4.
27.04.2011, 10:43
общий
27.04.2011, 11:01
Адресаты:
Хм, как-то выпустил из виду, что возможны отрицательные [$961$]...
Спасибо
Век живи - век учись... 
Спасибо
Век живи - век учись...
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
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