The area of the region defined byx-y- - -x-y- - 1- -x- - 1- -y- - 1 is

Quadrant 1: x ≥ 0, y ≥ 0 Then |x y|≤ 1 ⇒ x y ≤ 1 or x+y≤ 1 Quadrant 2: x ≤ 0, y ≥ 0 Then nbsp; | x y|≤ 1 ⇒ x y ≤ 1 or x+y≤ 1 Quadrant 3: x ≤ 0, y ≤ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Area between Two Curves

The area of t...

Question

The area of the region defined by
${(x, y) : | | x | - | y | | \leq 1, | x | \leq 1, | y | \leq 1}$ is

Open in App

Solution

Quadrant - 1: $x \geq 0, y \geq 0$
Then $| x - y | \leq 1$
$\Rightarrow x - y \leq 1$
or $- x + y \leq 1$

Quadrant - 2: $x \leq 0, y \geq 0$
Then $| - x - y | \leq 1$
$\Rightarrow - x - y \leq 1$
or $x + y \leq 1$

Quadrant - 3: $x \leq 0, y \leq 0$
Then $| - x + y | \leq 1$
$\Rightarrow - x + y \leq 1$
or $x - y \leq 1$

Quadrant - 4: $x \geq 0, y \leq 0$
Then $| x + y | \leq 1$
$\Rightarrow x + y \leq 1$
or $- x - y \leq 1$

$| | x | - | y | | \leq 1$

$| x | \leq 1; | y | \leq 1$

Area $= 2 \times 2 = 4 sq. units$

Suggest Corrections

Similar questions

Q. The area of the region bounded by

1 - y^{2} = | x |

and

| x | + | y | = 1

Q. The area of the region described by

A = (x, y) : x^{2} + y^{2} \leq 1

and

y^{2} \leq 1 - x

is:

Q. Area of the region

{(x, y) / x^{2} + y^{2} \leq 1 \leq x + y}

is:

Q. The area of the region

A = {(x, y) : 0 \leq y \leq x | x | + 1 and - 1 \leq x \leq 1}

in sq. units, is :

Q. The area of the region bounded by

y = | x - 1 |

and

y = 1

Join BYJU'S Learning Program

The area of the region defined by {(x,y):||x|−|y||≤1, |x|≤1, |y|≤1} is

The area of the region defined by
${(x, y) : | | x | - | y | | \leq 1, | x | \leq 1, | y | \leq 1}$ is