Area Under the Curve
Area Under Curves
nta_pyq_2025_jan
Grade 12
Question:
Consider the region R = {(x, y) : x \le y \le 9 - 11 2 x , x \ge 0} . 3 The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:
730 119
625 111
821 123
567 121
Step-by-Step Solution
Key Concept: Apply the core result for area bounded by curves and simplify using the given constraints.
t. (9 - 2 11t - t) 3 (4) 11 2 3 A = 9t - t - t 3 dA 2 = 9 - 2t - 11t dt 2 \Rightarrow 11t + 2t - 9 = 0 2 11t + 11t - 9t - 9 = 0 9 t = -1&t = 11 9 11 81 9 \therefore largest area = (9 - , - ) 11 3 121 11 9 63 567 = ⋅ = 11 11 121
Correct Answer: 4