Question

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

Answer 1

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.