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Образовательный студенческий форум _ Интегралы _ int (0 sin 1) ((arcsin x)^2 + 1)/(1 - x^2)^(1/2) dx
Автор: NadiN 22.4.2007, 5:45
int (0 sin 1) ((arcsin x)^2 + 1)/(1 - x^2)^(1/2) dx
Помогите, пожалуйста, решить определённый интеграл....
Не понимаю, где надо применять замену 
Автор: Lion 22.4.2007, 7:23
int (0 sin 1) ((arcsin x)^2 + 1)/(1 - x^2)^(1/2) dx =
= int (0 sin 1) ((arcsin x)^2 + 1) d(arcsin x) = | t = arcsin x | =
= int (0 1) (t^2 + 1) dt = (1/3 * t^3 + t)_{0}^{1} =
= (1/3 * 1^3 + 1) - (1/3 * 0^3 + 0) = 1/3 + 1 = 4/3.
Автор: NadiN 6.5.2007, 8:23
Спасибо 
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