Definite Integration
Grade None
Question:
<p>Let 2a > -1. If the area of the region of the plane defined by {(x, y) : x <span class="math-tex">\(\geq\)</span> 0, 2y - x <span class="math-tex">\(\geq\)</span> 0, ax + y - 3 <span class="math-tex">\(\leq\)</span> 0} is equal to 3, then the value of a, lies in :</p>
<p style="display:inline"><span class="math-tex">\(\left(\frac{3}{2}, \frac{5}{2}\right)\)</span></p>
<p style="display:inline"><span class="math-tex">\(\left(\frac{1}{2}, \frac{3}{4}\right)\)</span></p>
<p style="display:inline"><span class="math-tex">\(\left(\frac{5}{2}, \frac{10}{3}\right)\)</span></p>
<p style="display:inline"><span class="math-tex">\(\left(\frac{3}{4}, \frac{3}{2}\right)\)</span></p>
Step-by-Step Solution
Key Concept: Identify the vertices of the triangle formed by the boundary lines and use the geometric area formula, specifically treating the segment on the y-axis as the base, to solve for the parameter 'a'.
<p><span class="math-tex">$\left(\frac{3}{4}, \frac{3}{2}\right)$</span></p>
Correct Answer: D