Question

The integral \[ \int_{0}^{\pi/2}\frac{\sin x}{x^p}\,dx \] converges if ____.

• A. \(p>2\)
• B. \(p>3\)
• C. \(p<2\)
• D. \(p>4\)

Hint:

Whenever an improper integral involves \[ \sin x,\ \tan x,\ 1-\cos x \] near \(x=0\), use \[ \boxed{ \sin x\sim x,\qquad \tan x\sim x,\qquad 1-\cos x\sim\frac{x^2}{2}. } \]

Answer 1

The Correct Option is C