Question

If I₁ =$2\pi f(x)$ and I₂ =$f(4)f(x) = \sin^{2}x$, where | x | < 1, then which of the following statement is true –

• A. Neither I₁ nor I₂ exists
• B. I₁ exists and I₂ does not exists
• C. I₁ does not exists and I₂ exists
• D. None of these

Answer 1

Answer: (C)

I₁ does not exists and I₂ exists

Answer 2

We know $\frac { \tan ^ { - 1 } x } { x }$ < 1 and > 1, ∀ x ∈ R

∴ $\frac { \tan ^ { - 1 } x } { x }$ – < 0 and – $\frac { \tan ^ { - 1 } x } { x }$ > 0

⇒ I₁ does not exists and I₂ exists

Hence (3) is the correct answer.