If f(x) is a continuous function defined on [ – a,a] ,then prove that

Using interval addition property of integration, we know that

So L.H.S can be written as,

…..(1)

Now let us take x = – t

Differentiating it, we get,

dx = – dt

from above assumption

when x = – a t = a

and when x = 0 t = 0

Substituting the above assumptions in equation 1

Using the property of integration

…….(2)

Using integration property

…..(3)

Using equation 2 and 3, now equation 1 can be rewritten as

Now using the property

Hence proved.