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Консультация № 189464
22.05.2016, 07:26
0.00 руб.
1
1
1
Здравствуйте! У меня возникли сложности с таким заданием:
Дан
[$8747$][$8747$]f(x,y) dxdy. Записать в виде повторного и расставить пределы интегрирования в декартовых и полярных координатах.
Дан
[$8747$][$8747$]f(x,y) dxdy. Записать в виде повторного и расставить пределы интегрирования в декартовых и полярных координатах.
Прикрепленные файлы:
Обсуждение
22.05.2016, 10:02
общий
это ответ
Здравствуйте, YarLam125!
На использованном Вами рисунке изображены две окружности, радиусы которых
а центры находятся в начале координат и в точке 
Поэтому их уравнения в декартовой прямоугольной системе координат имеют вид 
и 
а в полярной системе координат - 
и 
Решая систему уравнений
вычислим декартовы координаты точек пересечения:
Окружности пересекаются в точках
( 
- в полярных координатах. Здесь удобно принять 
).
Область интегрирования описывается в декартовых координатах следующей системой неравенств:
Используя рисунок и результаты вычислений, можно установить, что в полярных координатах область интегрирования описывается следующей системой неравенств:
Следовательно,
С уважением.
На использованном Вами рисунке изображены две окружности, радиусы которых
а центры находятся в начале координат и в точке Поэтому их уравнения в декартовой прямоугольной системе координат имеют вид и а в полярной системе координат - и Решая систему уравненийОкружности пересекаются в точках
( - в полярных координатах. Здесь удобно принять ). Область интегрирования описывается в декартовых координатах следующей системой неравенств:
Используя рисунок и результаты вычислений, можно установить, что в полярных координатах область интегрирования описывается следующей системой неравенств:
Следовательно,
С уважением.
5
Спасибо!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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