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Консультация № 187335
14.05.2013, 15:23
91.28 руб.
0
4
4
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Заранее всем спасибо!
Если плохо видно
Заранее всем спасибо!
Если плохо видно
Обсуждение
14.05.2013, 16:01
общий
это ответ
Здравствуйте, Илья!
2.
Искомый интеграл
I=[$8747$]-11dx[$8747$]x^2-10(x3-2y)dy=
=[$8747$]-11dx(x3y-y2)|y=x^2-1y=0=
=[$8747$]-11dx(-x3(x2-1)+(x2-1)2)=
=[$8747$]-11(-x5+x3+x4-2x2+1)dx
Так как интеграл от нечетной функции в симметричных пределах равен нулю, а от четной - удвоенному интегралу по положительной части отрезка, то
I=2[$8747$]01(x4-2x2+1)dx=2((x5/5)-2(x3/3)+x)|01=2((1/5)-(2/3)+1)=16/15
2.
Искомый интеграл
I=[$8747$]-11dx[$8747$]x^2-10(x3-2y)dy=
=[$8747$]-11dx(x3y-y2)|y=x^2-1y=0=
=[$8747$]-11dx(-x3(x2-1)+(x2-1)2)=
=[$8747$]-11(-x5+x3+x4-2x2+1)dx
Так как интеграл от нечетной функции в симметричных пределах равен нулю, а от четной - удвоенному интегралу по положительной части отрезка, то
I=2[$8747$]01(x4-2x2+1)dx=2((x5/5)-2(x3/3)+x)|01=2((1/5)-(2/3)+1)=16/15
14.05.2013, 16:20
общий
это ответ
Здравствуйте, Илья!
3
Область интегрирования - правый полукруг единичного радиуса с центром в начале координат.
3
Область интегрирования - правый полукруг единичного радиуса с центром в начале координат.
.
Форма ответа
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