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.