The area of the region x,y/x2+y2≤1≤x+y

S≡x2+y2−1≤0L≡x+y−1≥0Req. Area =14 (Area of circle ) – (Area of triangle OAB) =14π12−1211=π4−12

The area of the region x,y/x2+y2≤1≤x+y

S≡x2+y2−1≤0L≡x+y−1≥0Req. Area =14 (Area of circle ) – (Area of triangle OAB) =14π12−1211=π4−12

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The area of the region $\{(x, y) / x^{2} + y^{2} \leq 1 \leq x + y\}$

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$\frac{π}{4} + \frac{1}{2}$

$π + 1$

$\frac{π}{4} - \frac{1}{2}$

$\frac{π}{4} + \frac{3}{4}$

answer is C.

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Detailed Solution

$S \equiv x^{2} + y^{2} - 1 \leq 0$

$L \equiv x + y - 1 \geq 0$

Req. Area $= \frac{1}{4}$ (Area of circle ) – (Area of triangle OAB)

$= \frac{1}{4} π {(1)}^{2} - \frac{1}{2} (1) (1)$

$= \frac{π}{4} - \frac{1}{2}$

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The area of the region $\{(x, y) / x^{2} + y^{2} \leq 1 \leq x + y\}$