If f x = sin ⁡ x , g x = cos ⁡ x and h x = c o s cos ⁡ x , then the integral Ι = ∫ f g x . f x . h x d x simplifies to - λ sin 2 ⁡ cos ⁡ x + C (where, C is the constant of integration). The value of λ is equal to

Question

If f x = sin ⁡ x , g x = cos ⁡ x and h x = c o s cos ⁡ x , then the integral Ι = ∫ f g x . f x . h x d x simplifies to - λ sin 2 ⁡ cos ⁡ x + C (where, C is the constant of integration). The value of λ is equal to,

MARKS App · Accepted Answer

Given integral, Ι = ∫ s i n cos ⁡ x . sin ⁡ x . c o s cos ⁡ x d x Let, s i n cos ⁡ x = t ⇒ - c o s cos ⁡ x . sin ⁡ x d x = d t ∴ Ι = ∫ - t d t = - t 2 2 + C = C - s i n 2 cos ⁡ x 2

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