Question

Area of the region bounded by the curve y = cosx between x = 0 and x = π is ______.

Options

• 2 sq.units

• 4 sq.units

• 3 sq.units

• 1 sq.units

Answer 1

Area of the region bounded by the curve y = cosx between x = 0 and x = π is 2 sq.units.

Explanation:

Given that: y = cos x, x = 0, x = π

Required area = `int_0^(pi/2) cos x  "d"x + |int_(pi/2)^pi cos x  "d"x|`

= `[sin x]_0^(pi/2) + |(sin x)_(pi/2)^pi|`

= `[sin  pi/2 - sin 0] + |[sin pi - sin  pi/2]|`

= `(1 - 0) + |0 - 1|`

= 1 + 1

= 2 sq.units