COMEDK · Maths · 31. Area Under Curves
The area of the region bounded by the curve \(y^2=2 y-x\) and the \(y\)-axis is
- A 1 sq unit
- B \(\dfrac{20}{3}\) sq units
- C 2 sq units
- D \(\dfrac{4}{3}\) sq units
Answer & Solution
Correct Answer
(D) \(\dfrac{4}{3}\) sq units
Step-by-step Solution
Detailed explanation
The given equation of the curve is \(y^2 = 2y - x\), which can be rewritten as \(x = 2y - y^2\). The curve intersects the \(y\)-axis where \(x = 0\). Setting \(x = 0\) in the equation \(x = 2y - y^2\), we get \(2y - y^2 = 0\), which implies \(y(2 - y) = 0\). Thus, the points of…
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