Question:
Using the method of integration find the area bounded by the curve x + y = 1 . [Hint: The required region is bounded by lines x + y = 1, x- y = 1, - x + y = 1 and - x - y = 1].
Answer:
Given Curve is |x| + |y| = 1
This function has 4 cases:
1. x + y = 1
2. -x + y = 1
3. x - y = 1
4. -x - y = 1
Now when we solve these equation taken two at a time, we get the points
(0,1), (1,0), (0,-1), (-1,0)
When we plot it, we form a square and it is also symmetrical about a nd y-axis.
Now area A is defined as
A = 4* 1∫0 (1-x) dx
=> A = 4 *[x - x2 /2 0]1
=> A = 4[1- 1/2 - 0]
=> A = 4/2
=> A = 2
So required area is 2 unit2
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