f(x,y)=sgn(x-y)求F(y)=∫f(x-y)dx积分从0到1y大于1＆小于0的情况很简单,函数是1和－1两条直线,那么y在0和1之间呢?表达式怎么求?

Question

f(x,y)=sgn(x-y)求F(y)=∫f(x-y)dx积分从0到1
y大于1＆小于0的情况很简单,函数是1和－1两条直线,那么y在0和1 之间呢?表达式怎么求?

Answer 1

0≤y≤1时,
F(y)=∫[0,1]f(x-y)dx
=∫[0,y]f(x-y)dx+∫[y,1]f(x-y)dx
=∫[0,y](-1)dx+∫[y,1]1dx
=-y+1-y
=1-2y.