<p>The value of ∫₋₁¹ [x[1 + sin πx] + 1] dx is ([·] denotes the greatest integer)</p>
Step-by-Step Solution
Key Concept: Separate the integral into parts: recognize that the first term is an odd function and the second is constant.
<p>For x ∈ [-1, 1]: sin πx ranges from -sin π to sin π. Since [1 + sin πx] gives the greatest integer of (1 + sin πx), and considering symmetry properties, ∫₋₁¹ [x[1 + sin πx]] dx = 0 (odd function). Thus ∫₋₁¹ 1 dx = 2.</p>
Correct Answer: A