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KVPY2020MathematicsDefinite Integration

The value of the integral ∫ 1 3 ( x - 2 ) 4 sin 3 ( x - 2 ) + ( x - 2 ) 2019 + 1 d x is

Options

  1. A0
  2. B2
  3. C4
  4. D5

Correct answer

B. 2

Step-by-step solution

∫ 1 3 ( x - 2 ) 4 sin 3 ( x - 2 ) + ( x - 2 ) 2019 + 1 d x x - 2 = t ⇒ d x = d t ∫ - 1 1 t 4 sin 3 t + t 2019 + 1 d t = ∫ - 1 1 d t = t - 1 1 = 2

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