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Консультация № 67275
16.12.2006, 18:36
0.00 руб.
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3
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Уважаемые Эксперты, очень прошу, пожалуйста, помогите, если вас не затруднит сделать данное задание!
Вычислить определенные интегралы:
1. от 1 до10 ∫ 1+x+x^2 / x dx
2. от 0 до 1 ∫ e^x dx / √(1+e^(2x)
3. от 0 до 1 (x+10) e^(-x) dx∫
Вычислить определенные интегралы:
1. от 1 до10 ∫ 1+x+x^2 / x dx
2. от 0 до 1 ∫ e^x dx / √(1+e^(2x)
3. от 0 до 1 (x+10) e^(-x) dx∫
Обсуждение
Неизвестный
16.12.2006, 19:08
общий
это ответ
Здравствуйте, XDRIVE!
1)∫1/x dx +∫dx + ∫xdx = (lnx + x + x^2/2) от 1 до 10 = ln10 + 10 +50 - 0 - 1 - 1/2) = ln10 + 58.5
3) интеграл берем по частям
u=10+x dv=e^(-x)dx du=dx v=-e^(-x)
∫(x+10) e^(-x) dx = (-(x+10)*e^(-x)) от 0 до 1 - ∫(-e^(-x)dx= -11*1/e + 10 - (e^(-x)) от 0 до 1 = -11*1/e +10 - 1/e +1 = -12*1/e +11
1)∫1/x dx +∫dx + ∫xdx = (lnx + x + x^2/2) от 1 до 10 = ln10 + 10 +50 - 0 - 1 - 1/2) = ln10 + 58.5
3) интеграл берем по частям
u=10+x dv=e^(-x)dx du=dx v=-e^(-x)
∫(x+10) e^(-x) dx = (-(x+10)*e^(-x)) от 0 до 1 - ∫(-e^(-x)dx= -11*1/e + 10 - (e^(-x)) от 0 до 1 = -11*1/e +10 - 1/e +1 = -12*1/e +11
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