CUET · MATHS · PYQ PAPER 2023
The area of the region bounded by \(y=2 x-x^2\) and \(x\)-axis is :
- A \(\frac{2}{3}\) sq. units
- B \(\frac{4}{3}\) sq. units
- C \(\frac{4}{5}\) sq. units
- D \(\frac{5}{3}\) sq. units
Answer & Solution
Correct Answer
(B) \(\frac{4}{3}\) sq. units
Step-by-step Solution
Detailed explanation
\(2x-x^2=0 \implies x(2-x)=0 \implies x=0, x=2\) \(A = \int_{0}^{2} (2x - x^2) dx\) \(A = \left[ x^2 - \frac{x^3}{3} \right]_{0}^{2} = \left( 2^2 - \frac{2^3}{3} \right) - (0) = 4 - \frac{8}{3} = \frac{12-8}{3} = \frac{4}{3}\)
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