The area (in sq. units) bounded between y = 3 sin ⁡ x and y = - 4 sin 3 ⁡ x from x = 0 to x = π is

Step-by-step solution

As 3 sin ⁡ x ≥ 0 and - 4 sin 3 ⁡ x ≤ 0 ∀ x ∈ 0 , π , the required area is A = ∫ 0 π 3 sin ⁡ x - - 4 sin 3 ⁡ x d x A = ∫ 0 π 3 sin ⁡ x + ( 3 sin ⁡ x - sin ⁡ 3 x ) d x = ∫ 0 π 6 sin ⁡ x - sin ⁡ 3 x d x = - 6 cos ⁡ x + cos ⁡ ( 3 x ) 3 π 0 = 6 - 1 3 - - 6 + 1 3 = 12 - 2 3 = 34 3 sq. units