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Консультация № 83945
24.04.2007, 13:12
0.00 руб.
0
3
3
Здравствуйте!
У меня имеется простенький пример: интеграл (dx/sqrt(1-2x^2)
я хочу его свести к табличному интеграл (du/sqrt(a^2+u^2))
мое решение:
интеграл (dx/sqrt(2(1/2-x^2))= 1/sqrt(2) arcsin(x/sqrt(2))
делаю проверку и не могу найти ошибку...
подскажите пожалуйста, я не думаю что из под корня нельзя выносить...
У меня имеется простенький пример: интеграл (dx/sqrt(1-2x^2)
я хочу его свести к табличному интеграл (du/sqrt(a^2+u^2))
мое решение:
интеграл (dx/sqrt(2(1/2-x^2))= 1/sqrt(2) arcsin(x/sqrt(2))
делаю проверку и не могу найти ошибку...
подскажите пожалуйста, я не думаю что из под корня нельзя выносить...
Обсуждение
Неизвестный
24.04.2007, 13:40
общий
это ответ
Здравствуйте, Zhiriki!
Просто Вы не верно находите константу <b>a</b>.
∫ (dx/√(1-2x^2) = ∫ (dx/√(2(1/2-x<sup>2</sup>)) =
= {приводим знаменатель к виду (a<sup>2</sup>-x<sup>2</sup>)} =
= 1/√2 ∫ (dx/√((1/√2)<sup>2</sup> - x<sup>2</sup>) =
= {применяем стандартную формулу} = 1/√2 arcsin (x/(1/√2)) = 1/√2 arcsin (√(2) x).
Good Luck!!!
Просто Вы не верно находите константу <b>a</b>.
∫ (dx/√(1-2x^2) = ∫ (dx/√(2(1/2-x<sup>2</sup>)) =
= {приводим знаменатель к виду (a<sup>2</sup>-x<sup>2</sup>)} =
= 1/√2 ∫ (dx/√((1/√2)<sup>2</sup> - x<sup>2</sup>) =
= {применяем стандартную формулу} = 1/√2 arcsin (x/(1/√2)) = 1/√2 arcsin (√(2) x).
Good Luck!!!
Неизвестный
24.04.2007, 20:17
общий
это ответ
Здравствуйте, Zhiriki! Во-первых надо сводить к другому
табличному интегралу : ?du/sqrt(a^2-u^2) , ?-знак интеграла .
?dx/sqrt(1-2x^2)=(1/sqrt2)*?[(sqrt2*dx)/sqrt(1-2x^2)]=
=(1/sqrt2)*?(d(x*sqrt2))/sqrt(1-2x^2)=(1/sqrt2)*arcsin(x*sqrt2)+C.
С уважением Айболит.
табличному интегралу : ?du/sqrt(a^2-u^2) , ?-знак интеграла .
?dx/sqrt(1-2x^2)=(1/sqrt2)*?[(sqrt2*dx)/sqrt(1-2x^2)]=
=(1/sqrt2)*?(d(x*sqrt2))/sqrt(1-2x^2)=(1/sqrt2)*arcsin(x*sqrt2)+C.
С уважением Айболит.
Форма ответа
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