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Консультация № 187330
12.05.2013, 12:00
95.78 руб.
0
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Обсуждение
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12.05.2013, 22:07
общий
это ответ
Здравствуйте, Илья!
Раскладывая подинтегральную функцию, получим знакопеременный ряд
[$8730$](1+x2)=1+(x2/2)-(x4/8)+...
Для такого ряда погрешность при замене ряда частичной суммой не превосходит модуля первого отброшенного члена.
Если ограничиться двумя первыми слагаемыми, то погрешность не превысит величины x4/8.
Поэтому после интегрирования мы получим погрешность вычисления не более чем
[$8747$]01/2(x4/8)dx=(x5/40)|01/2=1/1280<0,0008. Это обеспечивает требуемую точность.
Таким образом, с нужной точностью, интеграл равен
[$8747$]01/2(1+(x2)/2)dx=(x+(x3)/6)|01/2=25/48=0,521...
Ответ: 0,521
Раскладывая подинтегральную функцию, получим знакопеременный ряд
[$8730$](1+x2)=1+(x2/2)-(x4/8)+...
Для такого ряда погрешность при замене ряда частичной суммой не превосходит модуля первого отброшенного члена.
Если ограничиться двумя первыми слагаемыми, то погрешность не превысит величины x4/8.
Поэтому после интегрирования мы получим погрешность вычисления не более чем
[$8747$]01/2(x4/8)dx=(x5/40)|01/2=1/1280<0,0008. Это обеспечивает требуемую точность.
Таким образом, с нужной точностью, интеграл равен
[$8747$]01/2(1+(x2)/2)dx=(x+(x3)/6)|01/2=25/48=0,521...
Ответ: 0,521
5
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