The area of the region of the plane bounded by `max(|x|,|y|)lt=1a n dx ylt=1/2` is `1/2+1n2s qdotu n i t s` (b) `3+1n2s qdotu n i t s` `(31)/4s qdotu n i t s` (d) `1+21n2s qdotu n i t s`

Options

A. `1//2` + In 2 sq. units
B. 3+ In 2 sq. units
C. `31//4` sq. units
D. 1+2 In 2 sq. units

Answer

B

Explanation

`max (|x|,|y|)le1rArr |x| le 1 and |y| le 1`
which represent square bounded by `x=pm1 and y=pm1`

The required area is the lined area.
Now, shaded area is given by
`2overset(1)underset(1//2)int(1-(1)/(2x))dx=2(x-(1)/(2)" In "x)^(1)`
`=2[(1-0)-((1)/(2)-(1)/(2)" In "(1)/(2))]`
`=1-" In " 2` sq. units.
or Horizontal lined area `=4-(1-" In "2)=3+" In "2`. sq. units.