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Задать вопрос экспертам

Консультация № 183216

17.05.2011, 20:23

110.07 руб.

17.05.2011, 20:31

0 5 4

Образование

Здравствуйте, уважаемые эксперты! не сложные но нужно-срочные интегралы.
[$8747$]dx/(x[$183$][$8730$](3x-3x² ))

[$8747$](3x+18)/(x³-6х²+18x) dx;
[$8747$]dx/(sin3x+4)
Вычислить интегралы или установить их расходимость: ₃⁶[$8747$]dx/[$8730$](x²-6x+9) интеграл от 3 до 6

Сделать чертеж и найти объем тела, ограниченного поверхностями z = 0, у = х и плоскостью, проходящей через точки А (3;9; 0), В (-3; 9 ; 0) и С (0; 0; 6). наверное тут еще нужно y=0 плоскость.

Найти общее решение уравнения:
(9+x²)[$183$]y'+3y=arctg 3/x

Обсуждение

Неизвестный

17.05.2011, 20:25

общий

Первый что-то не отобразился ∫dx/(x∙√(3x-3x^2 ))

давно

Roman Chaplinsky / Химик CH

Модератор
156417
2175

17.05.2011, 20:53

общий

это ответ

Здравствуйте, alya_koshka!
[$8747$]dx/(x[$183$][$8730$](3x-3x²)=[$8747$]dx/(x²[$183$][$8730$]3[$183$][$8730$](1/x-1)=
=(-1/[$8730$]3)[$183$](1/x-1)^-1/2d(1/x-1)=(-1/[$8730$]3)[$183$](1/(-1/2))[$183$](1/x-1)^1/2=(2/[$8730$]3)[$183$][$8730$](1/x-1)

₃⁶[$8747$]dx/[$8730$](x²-6x+9)=₃⁶[$8747$]dx/|x-3|=₃⁶[$8747$]d(x-3)/(x-3)=
=ln(x-3)|₃⁶=ln(6-3)-ln(3-3)=ln(3)-ln(0)=ln(3)+[$8734$]=[$8734$]
Интеграл расходится

давно

Коцюрбенко Алексей Владимирович

Старший Модератор
312929
1973

17.05.2011, 22:16

общий

это ответ

Здравствуйте, alya_koshka!

2. Разложим подинтегральное выражение на сумму простых дробей

откуда A = 1, B = -1, C = 9 и интеграл равен

3. Сделаем замену переменной t = tg 3x/2, x = 2/3 arctg t, dx = 2 dt/3(1+t[sup]2[/sup]), sin 3x = 2t/(1+t[sup]2[/sup]). Тогда

5

Спасибо.

давно

Киселев Виталий Сергеевич

Академик
324866
619

18.05.2011, 07:00

общий

это ответ

Здравствуйте, alya_koshka!

Будут вопросы обращайтесь в минифорум.
Удачи

5

Спасибо

давно

Гордиенко Андрей Владимирович

Мастер-Эксперт
17387
18345

18.05.2011, 12:13

общий

это ответ

Здравствуйте, alya_koshka!

Во избежание ошибок проверьте, пожалуйста, выкладки.

С уважением.

Об авторе:
Facta loquuntur.

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