Question

第五题怎么做

Answer 1

(5)
f(x)
=(1/2)sinx ; 0≤x≤π
=0 ; x<0 or x>π
To find: φ(x)=∫(0->x) f(t) dt
case 1: 0≤x≤π
φ(x)
=∫(0->x) (1/2)sint dt
=(1/2) [cost]|(0->x)
=(1/2)( cosx -1)
case 2: x<0
φ(x)
=∫(0->x) (1/2)sint dt
=-∫(x->0) (1/2)sint dt
=0
case 2: x>π
φ(x)
=∫(0->x) (1/2)sint dt
=∫(0->π) f(t) +∫(π->x) f(t) dt
=∫(0->π) (1/2)sint dt +∫(π->x) 0 dt
=∫(0->π) (1/2)sint dt
=(1/2)[ cost]|(0->π)
=-1
ie
φ(x)
=0 ; x<0
=(1/2)( cosx -1) ; 0≤x≤π
=-1 ; x>π

Answer 2

如下图所示