定积分证明题
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(5)
let
x=π/2 -t
dx=-dt
t=0, x=π/2
t=π/2, x=0
∫(0->π/2) f(sinx) dx
=∫(π/2->0) f(cost) (-dt)
=∫(0->π/2) f(cost) dt
=∫(0->π/2) f(cosx) dx
(7)
∫(a->a+T) f(x) dx
d/da { ∫(a->a+T) f(x) dx }
= f(a+T) - f(a)
=0
=> ∫(a->a+T) f(x) dx 与a无关
let
x=π/2 -t
dx=-dt
t=0, x=π/2
t=π/2, x=0
∫(0->π/2) f(sinx) dx
=∫(π/2->0) f(cost) (-dt)
=∫(0->π/2) f(cost) dt
=∫(0->π/2) f(cosx) dx
(7)
∫(a->a+T) f(x) dx
d/da { ∫(a->a+T) f(x) dx }
= f(a+T) - f(a)
=0
=> ∫(a->a+T) f(x) dx 与a无关
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