The area bounded by the curves |y+x|≤1,|y−x|≤1 and 2x2+2y2≥1 is __ sq.units

|y+x|≤1|y−x|≤1 and 2x2+22≥1 y+x=±1 y−x=±1x+y=1 y−x=1x+y=−1 −x+y=1−x−y=1 −x+y=−1x−y=1 Required Area = Area of square - area of circle=4⋅121.1−π122=2−π2

The area bounded by the curves |y+x|≤1,|y−x|≤1 and 2x2+2y2≥1 is __ sq.units

|y+x|≤1|y−x|≤1 and 2x2+22≥1 y+x=±1 y−x=±1x+y=1 y−x=1x+y=−1 −x+y=1−x−y=1 −x+y=−1x−y=1 Required Area = Area of square - area of circle=4⋅121.1−π122=2−π2

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The area bounded by the curves $| y + x | \leq 1, | y - x | \leq 1 and 2 x^{2} + 2 y^{2} \geq 1$ is __ sq.units

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$(2 - \frac{π}{2})$

$(4 - \frac{π}{2})$

$(2 + \frac{π}{2})$

$(4 + \frac{π}{2})$

answer is B.

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Detailed Solution

$| y + x | \leq 1 | y - x | \leq 1 and \begin{array}{ll} 2 x^{2} + 2^{2} \geq 1 \\ y + x = \pm 1 y - x = \pm 1 \\ x + y = 1 y - x = 1 \\ x + y = - 1 - x + y = 1 \\ - x - y = 1 - x + y = - 1 \\ x - y = 1 \end{array}$