The area (in sq. units) bounded between the curves y = e x cos ⁡ x and y = e x sin ⁡ x from x = π 4 to x = π 2 is

Step-by-step solution

As sin ⁡ x > cos ⁡ x ,   ∀ x ∈ π 4 , π 2 ⇒ e x sin ⁡ x > e x cos ⁡ x Thus the required area is A = ∫ π 4 π 2 e x sin ⁡ x - e x cos ⁡ x d x = - ∫ π 4 π 2 e x cos ⁡ x + - sin ⁡ x d x = - e x cos ⁡ x π 4 π 2 = − 0 − e π 4 ⋅ 1 2 = e π 4 2 As ∫ e x f x + f ′ x dx = e x ⋅ f x + C