Question

The area of the region bounded by y = |x - 2| and y = 2 is ______ 

पर्याय

• 2

• 4

• 1

• 3

Answer 1

The area of the region bounded by y = |x - 2| and y = 2 is 4. 

Explanation:

Required area = `int_0^4 (2 - |x - 2|)dx`

= `2int_0^4 dx - [int_0^2(2 - x)dx + int_2^4 (x - 2)dx]`

= `2[x]_0^4 dx - [[2x - x^2/2]_0^2 + [x^2/2 - 2x]_2^4]`

= 8 - [4 - 2 + (8 - 8) - (2 - 4)]

= 8 - 4 = 4