Area of the region bounded by the curve |x| + | vedclass

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Question

(C) The given equation is $|x| + y = 1$,which can be written as $y = 1 - |x|$.This equation represents two lines:$1$) For $x \ge 0$,$y = 1 - x$.$2$) F

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) The given equation is $|x| + y = 1$,which can be written as $y = 1 - |x|$.This equation represents two lines:$1$) For $x \ge 0$,$y = 1 - x$.$2$) For $x The region is bounded by these lines and the $x$-axis $(y = 0)$.The vertices of the region are $(0, 1)$,$(1, 0)$,and $(-1, 0)$.This forms a triangle with base length $b = 1 - (-1) = 2$ and height $h = 1$.The area of the triangle is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 2 	imes 1 = 1$ sq. units.

Area of the region bounded by the curve $|x| + y = 1$ is . . . . . . sq. units.

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