Question

The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 ≤ x ≤ `pi/2` is ______.

Options

• `sqrt(2)` sq.units

• `(sqrt(2) + 1)` sq.units

• `(sqrt(2) - 1)` sq.units

• `(2sqrt(2) - 1)` sq.units

Answer 1

The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 ≤ x ≤ `pi/2` is `(sqrt(2) - 1)` sq.units.

Explanation:

Given that y-axis, y = cos x, y = sin x, 0 ≤ x ≤ `pi/2`

Required area = `int_0^(pi/4) cos x  "d"x - int_0^(pi/4) sin x  "d"x`

= `[sin x]_0^(pi/4) - [- cos x]_0^(pi/4)`

= `[sin  pi/4 - sin 0] + [cos  pi/4 - cos 0]`

= `[1/sqrt(2) - 0 + 1/sqrt(2) - 1]`

= `2/sqrt(2) - 1`

= `(sqrt(2) - 1)` sq.units