五.记F(x)=nf(x),则F(x)=f(x) F(1)=n∫(x)dx=A,F(0)=0, Sdxf f(x)f(ydy=5o f(x dxf f(y)dy Sof()F(1)-F(x)ldx F(ilof()dx Jof(x)F(x)dx =42-51P(x)F(x)t=42-1F(x)dF(x) =A2-F2(x)= (1) 2 A A2 2 K心五. ( ) ( ) , 0 =  x 记F x f x dx 则F(x) = f (x), (1) ( ) , 1 0 F =  f x dx = A F(0) = 0,   =   1 1 0 1 1 0 ( ) ( ) ( ) ( ) x x dx f x f y dy f x dx f y dy =  − 1 0 f (x)[F(1) F(x)]dx =  −  1 0 1 0 F(1) f (x)dx f (x)F(x)dx  = −  1 0 2 A F (x)F(x)dx = −  1 0 2 A F(x)dF(x) 1 0 2 2 ( ) 2 1 = A − F x (1) 2 2 1 2 = A − F . 2 1 2 2 1 2 2 = A − A = A