# By using the properties of definite integrals, evaluate the integrals

Given:

As we can see f(x) = sin2x and f(-x) = sin2(-x) = (sin (-x))2 = (-sin x)2 = sin2x.

i.e. f(x) = f(-x)

so, sin2x is an even function.

It is also known that if f(x) is an even function then,

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