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99 Percentile Qs Bank for JEE MainMathematicsIndefinite Integration

If ∫ f x cos ⁡ x   d x = 1 2 f x 2 + c , then f x is

Options

  1. Ax + c
  2. Bsin ⁡ x + c
  3. Ccos ⁡ x + c
  4. Dc

Correct answer

B. sin ⁡ x + c

Step-by-step solution

Given, ∫ f x cos ⁡ x   d x = 1 2 f x 2 + c Differentiate both sides we get, f x cos ⁡ x = 1 2 ⋅ 2 f x f ′ ( x ) Then, f ′ x = cos ⁡ x Integrate both the sides we get, f x = sin ⁡ x + c

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