作者LuisSantos (^______^)
看板trans_math
标题Re: [积分]
时间Fri Mar 23 20:07:45 2007
※ 引述《king911015 (早已放弃爱上你)》之铭言：
: x f(t)
: Find a function f and a unmber a such that 6 + ∫ ----- dt =2√x for allx>0.
: a t^2
x f(t)
6 + ∫ ------ dt = (2)(√x)
a t^2
等号两边对 x 微分得
f(x) 1 1 1
------ = (2)(---)(----) = ----
x^2 2 √x √x
x^2
f(x) = -----
√x
t^2
f(t) = -----
√t
f(t) 1
------ = -----
t^2 √t
x 1
6 + ∫ ----- dt = (2)(√x)
a √t
x 1
∫ ----- dt = (2)(√x) - 6
a √t
|x
(2)(√t) | = (2)(√x) - 6
|a
(2)(√x) - (2)(√a) = (2)(√x) - 6
(-2)(√a) = -6 => √a = 3 => a = 3^2 = 9
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