F(x)=∫[x,0](x-2t)f(t)dt
=x∫[x,0]f(t)dt-2∫[x,0]tf(t)dt
F(-x)=(-x)∫[-x,0]f(t)dt-2∫[-x,0]tf(t)dt
z=-t,
=-x∫[x,0]f(-z)d(-z) -2∫[x,0] (-z)f(-z)d(-z)
=-x∫[x,0]f(z)dz +2∫[x,0]zf(z)dz
F(x)=-F(-x)
奇函数
F(x)=∫[x,0](x-2t)f(t)dt
=x∫[x,0]f(t)dt-2∫[x,0]tf(t)dt
F(-x)=(-x)∫[-x,0]f(t)dt-2∫[-x,0]tf(t)dt
z=-t,
=-x∫[x,0]f(-z)d(-z) -2∫[x,0] (-z)f(-z)d(-z)
=-x∫[x,0]f(z)dz +2∫[x,0]zf(z)dz
F(x)=-F(-x)
奇函数