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.


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