Using integration find the area of the region {(x,y)|x – 1| ≤ y ≤ √5 – x^{2}}.

To find area of region

{(x,y)|x – 1|≤y≤√5 – x^{2}}

|x – 1| = y

And x^{2} + y^{2} = 5 …(iii)

|x – 1|≤y≤√5 – x^{2}

|x – 1| = √5 – x^{2}

X = 2, – 1

Equation (i) and (ii) represent straight lines and equation (iii) is a circle with centre (0,0), meets axes at (±√5,0) and (0,±√5).

These are shown in the graph below: -

Required area = Region BCDB + Region CADC

The area of the region {(x,y)|x – 1|≤y≤√s – x^{2}} is

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