Area Under Curves
Region defined by multiple inequalities
MJAT_TS7_P2
Grade 12
Question:
Let $S=\{(x,y)\in\mathbb{R}\times\mathbb{R}: x\geq 0,\,y\geq 0,\,y^2\leq 4x,\,y^2\leq 12-2x,\,3y+8x\leq 58\}$. If the area of $S$ is $\alpha\sqrt{2}$, then $\alpha$ equals:
A) 172
B) 173
C) 174
D) 175
Step-by-Step Solution
Key Concept: Find the region $S$ bounded by: right parabola $y^2=4x$ and left parabola $y^2=12-2x$ (they intersect at $x=2$, $y=\pm 2\sqrt{2}$). Also constrained by line $3y+8x=58$. Compute the area by integration.
$\alpha=\mathbf{173}$. Answer: **B**.
Correct Answer: B