The area (in sq. units) bounded between y = 6 sin ⁡ x and y + 8 sin 3 ⁡ x = 0 from x = 0 to x = π is

Step-by-step solution

As 6 sin ⁡ x ≥ 0 and - 8 sin 3 ⁡ x ≤ 0   ∀ x ∈ 0 , π , The required area is A = ∫ 0 π 6 sin ⁡ x - - 8 sin 3 ⁡ x d x A = 2 ∫ 0 π 3 sin ⁡ x + 3 sin ⁡ x - sin ⁡ 3 x d x = 2 ∫ 0 π 6 sin ⁡ x - sin ⁡ 3 x d x = 2 - 6 cos ⁡ x + cos ⁡ 3 x 3 0 π = 2 6 - 1 3 - - 6 + 1 3 = 2 12 - 2 3 = 68 3 sq. units