Proove that: int _a^b f (x)dx= int_a^b f (a+b-x)dx ?

1 Answer
Apr 12, 2018

Let u=a+b−x

=> du=−dx

int_a^b f(x) dx = int_a^b f(u) du color(white)(ww

"changing limits, " ["when " u = a ; x=b]
color(white)(chenging lmwits [ "when " u = b ; x=a]

=> int_b^a f(a+b-x) (-dx)

=>- int_b^a f(a+b-x) dx

=> int_a^b f(a+b-x) dx

Hence Proved.