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Консультация № 189612
22.06.2016, 14:52
0.00 руб.
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9
1
Здравствуйте! У меня возникли сложности с таким вопросом:
вычислить площадь фигуры ограниченной линиями y=8+2x-x^2 y=2x+1
вычислить площадь фигуры ограниченной линиями y=8+2x-x^2 y=2x+1
Обсуждение
22.06.2016, 15:02
общий
Адресаты:
Если нарисуете графики функций, то увидите, что площадь равна
разности интегралов от параболы и прямой от одной точки пересечения до другой
разности интегралов от параболы и прямой от одной точки пересечения до другой
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
22.06.2016, 15:22
общий
23.06.2016, 12:11
это ответ
Здравствуйте, elena-grohotova12!
Найдем абсциссы точек пересечения линий, для этого решим уравнение: =8+2x-x2=2x+1.
Получим х1=[$8730$]7, х2=-[$8730$]7
Далее находим определенный интеграл от -[$8730$]7 до [$8730$]7 для разности функций : (8+2x-x2)-(2x+1)=
=7-x2. Первообразная полученной разности равна 7х-(x3)/3 + C
Тогда S=(7*[$8730$]7-(([$8730$]7)3)/3)-(7*(-[$8730$]7)-((-[$8730$]7)3)/3)=(28[$8730$]7)/3
Найдем абсциссы точек пересечения линий, для этого решим уравнение: =8+2x-x2=2x+1.
Получим х1=[$8730$]7, х2=-[$8730$]7
Далее находим определенный интеграл от -[$8730$]7 до [$8730$]7 для разности функций : (8+2x-x2)-(2x+1)=
=7-x2. Первообразная полученной разности равна 7х-(x3)/3 + C
Тогда S=(7*[$8730$]7-(([$8730$]7)3)/3)-(7*(-[$8730$]7)-((-[$8730$]7)3)/3)=(28[$8730$]7)/3
5
спасибо<br>
22.06.2016, 17:02
общий
Адресаты:
Как у Вас получилось, что при x1=3 и x2=-3 8+2x-x^2=2x+1?
Об авторе:
Facta loquuntur.
Facta loquuntur.
22.06.2016, 17:10
общий
Адресаты:
Скажем точнее: x = [$177$][$8730$]7, а не [$177$]3
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
22.06.2016, 17:15
общий
Адресаты:
Напишите исправленное решение в мини-форуме
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
22.06.2016, 20:10
общий
Найдем абсциссы точек пересечения линий, для этого решим уравнение: =8+2x-x^2=2x+1.
Получим х1=√7, х2=-√7
Далее находим определенный интеграл от -√7 до √7 для разности функций : (8+2x-x^2)-(2x+1)=
=7-x^2. Первообразная полученной разности равна 7х-(x^3)/3
Тогда S=(7*√7-(√7^3)/3)-(7*(-√7)-((-√7)^3)/3)=(28√7)/3
Получим х1=√7, х2=-√7
Далее находим определенный интеграл от -√7 до √7 для разности функций : (8+2x-x^2)-(2x+1)=
=7-x^2. Первообразная полученной разности равна 7х-(x^3)/3
Тогда S=(7*√7-(√7^3)/3)-(7*(-√7)-((-√7)^3)/3)=(28√7)/3
22.06.2016, 20:38
общий
Адресаты:
Если Вы находите первообразную, то не нужно забывать о постоянной интегрирования.
Об авторе:
Facta loquuntur.
Facta loquuntur.
23.06.2016, 12:07
общий
Адресаты:
Обратите внимание, решение исправлено
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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