Question

定积分证明题：f(x)在闭区间a到b上连续,求证：,∫b到a f(x)dx=,∫b到a f(a+b-x)dx

Answer 1

令a+b-x=t

对于区间端点：

x=b,t=a

x=a,t=b

所以,∫b到a f(a+b-x)dx = ,∫a到b f(t)dt

则

,∫b到a f(x)dx=,∫b到a f(a+b-x)dx