Question
Find the area of the region enclosed by the curves : y =
0, x = |y| and y = |x - 2|.Solution
We know that y = 0 is 'x-axis'. Now, for x = |y|, 'y' will be positive for any value of 'x'. So, essentially its only x = y but without any negative values of 'y'. So, we will get a 'V' shape graph along the 'y' axis. Similarly, y = |x - 2|, will be 'V' shaped along the 'x-axis' and since, we are subtracting -2, the origin of the line will move from (0,0) to (2,0). So, required area = Area of triangle So, Area of triangle = (1/2) X 2 X 1 = 1 square units
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