Question

Using integration find the area of the region {(x, y)|x – 1| ≤ y ≤ √5 – x²}.

Answer 1

To find area of region

{(x, y)|x – 1|≤ y ≤ √5 – x²}

|x – 1| = y

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