Area Under the Curve
Area bounded by multiple curves
Grade 12
Question:
<p>The area of the region bounded in first quadrant by \(y = x^{1/3}\), \(y = -x^2 + 2x + 3\), \(y = 2x - 1\) and the axis of ordinates is</p>
<p>(A) \(\frac{12}{55}\)</p>
<p>(B) \(\frac{55}{124}\)</p>
<p>(C) \(\frac{32}{55}\)</p>
<p>(D) None of these</p>
Step-by-Step Solution
Key Concept: Determine which curves bound the region in each interval; integrate the difference of upper and lower functions.
<p>Identify the region in the first quadrant bounded by the four given curves. Find intersection points of the parabola $y = -x^2 + 2x + 3$, line $y = 2x - 1$, and curve $y = x^{1/3}$. Set up integrals over appropriate intervals and compute to get area = $\frac{32}{55}$.</p>
Correct Answer: C