Question

Find the area bounded by the curve y = 2cosx and the x-axis from x = 0 to x = 2π

Answer 1

Given equation of the curve is y = 2 cos x

∴ Area of the shaded region = `int_0^(2pi) 2 cos x  "d"x`

= `int_0^(pi/2) 2 cos x  "d"x + int_(pi/2)^((3pi)/2) |2 cos x|"d"x + int_((3pi)/2)^(2pi) 2 cos x  "d"x`

= `2[sin x]_0^(pi/2) + |[2 sin x]_(pi/2)^((3pi)/2)| + 2[sin x]_((3pi)/2)^(2pi)`

= `2[sin  pi/2 - sin 0] + |2(sin  (3pi)/2 - sin  pi/2)| + 2[sin 2pi - sin  (3pi)/2]`

= `2(1) + |2(-1 - 1)| + 2(0 + 1)`

= 2 + 4 + 2

= 8 sq.units