Question

Find the area enclosed by

y = |x|, |x| = 1 and y = 0.


(a) 2

(b) 4

(c) 27

(d) 18

(e) 1


✔️✔️ quality answer needed✔️✔️

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Answer 1

Answer:

Drawing the graphs of the given data gives us the intersection which is shown in the attachments .

y = |x|

So y must be a positive number and can never be negative in this case .

|x| = 1 and hence x may be + 1 or - 1 .

But y has to be positive and hence we will not go down the x coordinate to include the value of y .

We see that the area enclosed by the graph shows two triangles whose base and height are one units each .

Area = 1/2 × base × height

⇒ 1/2 × 1 × 1 units²

⇒ 1/2 units²

Area of 2 such triangles = 2×1/2 units²

⇒ 1 units².

Area enclosed by the figure will be 1 units square .

OPTION E is the correct answer .

Step-by-step explanation:

In the first quadrant , the value of both x and y is positive .

In the second quadrant , the value of x is negative while y is positive .

In the third quadrant , the value of x is negative and y is negative .

In the fourth quadrant , the value of x is positive and y is negative .

Now we need to put the values which satisfy the given equation .

Answer 2

required area is the area of two triangles with vertices (0,0).(1,0),(1,1) and (0,0),(-1,0),(-1,1)

so area of the two triangles with base 1 height 1

2x1/2 xbxh =1×1×1=1