f(x)在[0,1]有连续的导数,f(0)=1,且∫∫f'(x+y)dxdy=∫∫f(t)dxdy,积分区域Dt={(x,y)|0
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f(x)在[0,1]有连续的导数,f(0)=1,且∫∫f''(x+y)dxdy=∫∫f(t)dxdy,积分区域Dt={(x,y)|0f(x)在[0,1]有连续的导数,f(0)=1,且∫∫f''(x+y)d
f(x)在[0,1]有连续的导数,f(0)=1,且∫∫f'(x+y)dxdy=∫∫f(t)dxdy,积分区域Dt={(x,y)|0
f(x)在[0,1]有连续的导数,f(0)=1,且∫∫f'(x+y)dxdy=∫∫f(t)dxdy,积分区域Dt={(x,y)|0
f(x)在[0,1]有连续的导数,f(0)=1,且∫∫f'(x+y)dxdy=∫∫f(t)dxdy,积分区域Dt={(x,y)|0
∫∫f(t)dxdy=f(t)∫∫dxdy=t^2f(t)/2
∫∫f'(x+y)dxdy=∫(0,t)dv∫(0,t)f'(u)du=∫(0,t)(f(t)-1)dv=t(f(t)-1)
由t(f(t)-1)=t^2f(t)/2得:f(t)-1=tf(t)/2
f(t)=2/(2-t)
f(x)=2/(2-x) (0
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