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The value of the integral Ι = ∫ e x sin ⁡ x + cos ⁡ x d x is equal to e x ⋅ f x + C , C being the constant of integration. Then the maximum value of y = f x 2 ,   ∀ x ∈ R is equal to

Options

  1. A0
  2. B- 1
  3. C1
  4. D1 2

Correct answer

C. 1

Step-by-step solution

As we know, ∫ e x f x + f ' x d x = e x ⋅ f x + C Thus, ∫ e x sin ⁡ x + cos ⁡ x d x = e x ⋅ sin ⁡ x + C i.e. f x = sin ⁡ x Hence, f x 2 = s i n x 2 : which has the maximum value of ‘1’

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