If f is an integrable function such that f(2a – x) = f(x), then prove that
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
Since, f(2a – x) = f(x)
Hence proved.