Definite Integration
Integrals Involving Greatest Integer Function
Grade 12
Question:
<p>The value of <span>\(\int_0^{\pi} [2\sin x] dx\)</span> where [ ] represents the greatest integer function is</p>
<p>(A) \(-5/3\)</p>
<p>(B) \(-\pi\)</p>
<p>(C) \(5/3\)</p>
<p>(D) \(-2\)</p>
Step-by-Step Solution
Key Concept: Determine where $2\sin x$ takes integer values and partition the integral accordingly.
<p><strong>IIT - 1995</strong></p>
Correct Answer: B