If f(x) is a continuous function defined on [0,2a]. Then Prove that

Question

Philoid · Accepted Answer

Using interval addition property of integration, we know that

So L.H.S can be written as,

Let us assume x = 2a – t

Differentiating it we get,

dx = – dt

from above assumption

when x = 2a t = 0

and when x = a t = a

substituting above assumptions in L.H.S

Using the property of integration

Using integration property

Substituting above value in equation 1

Now using the property

∴L.H.S = R.H.S

Hence, proved.