COMEDK · Maths · 31. Area Under Curves
The area of the region bounded by the line \(y = x + 2\) and the curve \(x = -y^2\) is
- A \(4.5\ \text{sq units}\)
- B \(13.5\ \text{sq units}\)
- C \(\dfrac{7}{6}\ \text{sq units}\)
- D \(2.5\ \text{sq units}\)
Answer & Solution
Correct Answer
(A) \(4.5\ \text{sq units}\)
Step-by-step Solution
Detailed explanation
The given curves are \(x = -y^2\) and \(y = x + 2\). To find the points of intersection, substitute \(x = y - 2\) into the equation of the parabola: \(y - 2 = -y^2\) \(y^2 + y - 2 = 0\) \((y + 2)(y - 1) = 0\) The points of intersection are at \(y = -2\) and \(y = 1\). The area…
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