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  4. The area of the region for which 0 < y < 3-2x-x2 and x>0 is

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Q. The area of the region for which $0 < y < 3-2x-x^{2}$ and $x>0$ is

NTA AbhyasNTA Abhyas 2022

Solution:

Area $=\int\limits _{0}^{1}\left(3 - 2 x - x^{2}\right)dx=\left(3 x - x^{2} - \frac{x^{3}}{3}\right)_{0}^{1}$
Solution
$=3-1-\frac{1}{3}=\frac{5}{3}$