Let be the bounded area enclosed by the curves and -axis that lies in the first quadrant. Let be the bounded area enclosed by the curves , , , and -axis that lies in the first quadrant. Then is equal to [2026]

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Solution

Q.
Let $A_{1}$ be the bounded area enclosed by the curves $y = x^{2} + 2,$ $x + y = 8$ and $y$ -axis that lies in the first quadrant. Let $A_{2}$ be the bounded area enclosed by the curves $y = x^{2} + 2$ , $y^{2} = x$ , $x = 2$ , and $y$ -axis that lies in the first quadrant. Then $A_{1} - A_{2}$ is equal to [2026]

1 $\frac{2}{3} (\sqrt{2} + 1)$

2 $\frac{2}{3} (4 \sqrt{2} + 1)$

3 $\frac{2}{3} (3 \sqrt{2} + 1)$

4 $\frac{2}{3} (2 \sqrt{2} + 1)$

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