Application of Integrals · Question 29

The area (in sq. units) of the region \(x, y) : 0 y 2|x| + 1, 0 y x2 + 1, |x| 3\ is

1. 323
2. 643
3. 173
4. 803

Answer

(2) 643

Solution

The region is symmetric about the y-axis. For x 0: 0 y (2x + 1, x2 + 1).

x2 + 1 2x + 1 x(x - 2) 0 0 x 2

Area for 0 x 3 = 02(x2 + 1) dx + 23(2x + 1) dx

= [ x33 + x ]02 + [x2 + x ]23

= 143 + (12 - 6) = 323

Required area = 2 323 = 643

Answer: (2)