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Консультация № 198131
03.04.2020, 15:43
0.00 руб.
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1
Здравствуйте! У меня возникли сложности с таким вопросом:
Вычислить криволинейный интеграл ϕL x2ydx – (y2+x)dy, где L – треугольник АОВ. {А(3;0),В(3;1),О(0;0)}
Вычислить криволинейный интеграл ϕL x2ydx – (y2+x)dy, где L – треугольник АОВ. {А(3;0),В(3;1),О(0;0)}
Обсуждение
08.04.2020, 05:10
общий
это ответ
Здравствуйте, fm11!
Искомый интеграл вычисляется как сумма интегралов по отрезкам AO, OB и BA.
На отрезке AO y=0, dy=0, x изменяется от 3 до 0, поэтому
На отрезке OB y=x/3, dy=dx/3, x изменяется от 0 до 3, следовательно
Наконец, на BA x=3, dx=0, y изменяется от 1 до 0, соответственно
Тогда криволинейный интеграл будет равен
Искомый интеграл вычисляется как сумма интегралов по отрезкам AO, OB и BA.
На отрезке AO y=0, dy=0, x изменяется от 3 до 0, поэтому
На отрезке OB y=x/3, dy=dx/3, x изменяется от 0 до 3, следовательно
Наконец, на BA x=3, dx=0, y изменяется от 1 до 0, соответственно
Тогда криволинейный интеграл будет равен
5
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