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If the integral Ι = ∫ x s i n x c o s x ⋅ ln ⁡ x + s i n x x dx = f x g x + c ∀ x > 0 , then the range of y = g x is (where, c is an arbitrary constant)

Options

  1. A- 1,1
  2. B0,1
  3. C0,1
  4. D- 1,1

Correct answer

A. - 1,1

Step-by-step solution

Let x sin ⁡ x = t ; then, I = ∫ d t = t + c = x sin ⁡ x + c Hence, range of sin x ∈ [ - 1 , 1 ]

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