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Using integration find the area of the region {(x,y)|x – 1| ≤ y ≤ √5 – x2}.
To find area of region
{(x,y)|x – 1|≤y≤√5 – x2}
|x – 1| = y
And x2 + y2 = 5 …(iii)
|x – 1|≤y≤√5 – x2
|x – 1| = √5 – x2
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 – x2} is