Definite Integration
Integrals Involving Greatest Integer Function
Grade 12
Question:
<p>If for a real number y, [y] is the greatest integer less than or equal to y, then the value of the integral <span>\(\int_0^{3\pi/2} [2\sin x] dx\)</span> is</p>
<p>(A) \(-\pi\)</p>
<p>(B) 0</p>
<p>(C) \(-\pi/2\)</p>
<p>(D) \(\pi/2\)</p>
Step-by-Step Solution
Key Concept: Partition the interval based on where $2\sin x$ crosses integer values and integrate piecewise.
<p><strong>IIT - 1999</strong></p>
Correct Answer: C