Evaluate:

Let,

Now

Let

Put x = -x in f(x)

As, (-x)² = (x)² and |-x| = |x|, we get,

⇒f(-x) = - f(x)

As f(-x) = - f(x)

So, f(x) is an odd function

We know that if g(x) is an odd function-

Therefore, I₁ = 0

Now

Let

Put x = -x in g(x)

As, (-x)² = (x)² and |-x| = |x|, we get,

As, g(-x) = g(x)

So, g(x) is an even function.

We know that if h(x) is an even function-

⇒ I₂ = 2(log 2 – log 1)

⇒ I₂ = 2log 2

Therefore, I = 2 log 2