f(x)=x^2 x<=0 1+2x x>0 求积分∫0-->2[f(x-1)]dx

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f(x)=x^2x<=01+2xx>0求积分∫0-->2[f(x-1)]dxf(x)=x^2x<=01+2xx>0求积分∫0-->2[f(x-1)]dxf(x)=x^2x<=01+2xx>0求积分∫0

f(x)=x^2 x<=0 1+2x x>0 求积分∫0-->2[f(x-1)]dx
f(x)=x^2 x<=0 1+2x x>0 求积分∫0-->2[f(x-1)]dx

f(x)=x^2 x<=0 1+2x x>0 求积分∫0-->2[f(x-1)]dx
f(x)=x^2 x<=0
1+2x x>0
∫0-->2[f(x-1)]dx
令x-1=t
x=0,t=-1;
x=2,t=1
原式=∫(-1,1)f(t)dt
=∫(-1,0)t²dt+∫(0,1)(1+2t)dt
=t³/3|(-1,0)+(t+t²)|(0,1)
=0-(-1/3)+1+1-0
=1/3+2
=7/3