第1个回答 2020-11-29
(6)
f(x)
=x^2 ; 0≤x≤1
=x ; 1≤x≤2
∫(0->x) f(t) dt , x∈[0,2]
case 1: 0≤x≤1
∫(0->x) f(t) dt
=∫(0->x) t^2 dt
=(1/3)x^3
case 2: 1≤x≤2
∫(0->x) f(t) dt
=∫(0->1) t^2 dt + ∫(1->x) t dt
=1/3 +(1/2)(x^2 -1)
(7)
f(x)
=(1/2)sinx ; 0≤x≤π
=0 ; x<0 or x>π
case 1: x<0
∫(0->x) f(t) dt =0
case 2: 0≤x≤π
∫(0->x) f(t) dt
=∫(0->x) (1/2)sint dt
=(1/2)[cost]|(0->x)
=(1/2)(cosx -1)
case 3: x>π
∫(0->x) f(t) dt
=∫(0->π) (1/2)sint dt +∫(π->x) 0 dt
=(1/2)[cost]|(0->π) +0
=-1
第2个回答 2020-11-29
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