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NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

The value of the integral ∫ x   1 3 1 - x 3 d x is equal to (where c is the constant of integration)

Options

  1. A6 x 4 3 8 + 3 11 x 11 6 + 3 14 x 7 3 + 1 17 x 17 6 + c
  2. B6 x 4 3 8 - 3 11 x 11 6 + 3 14 x 7 3 - 1 17 x 17 6 + c
  3. C2 x 4 3 8 - 3 11 x 4 6 - 3 14 x 7 3 - 1 17 x 17 6 + c
  4. D2 x 4 8 - 3 11 x 11 - 3 14 x 7 - 1 17 x 17 + c

Correct answer

B. 6 x 4 3 8 - 3 11 x 11 6 + 3 14 x 7 3 - 1 17 x 17 6 + c

Step-by-step solution

Let, I = ∫ x 1 3 1 - x 3 d x Let, x = t 6 ⇒ d x = 6 t 5 d t I = ∫ t 2 1 - t 3 3 6 t 5 d t I = 6 ∫ t 7 1 - 3 t 3 + 3 t 6 - t 9 d t = 6 ∫ t 7 - 3 t 10 + 3 t 13 - t 16 d t I = 6 t 8 8 - 3 t 11 11 + 3 t 14 14 - t 17 17 + c I = 6 x 4 3 8 - 3 11 x 11 6 + 3 14 x 7 3 - 1 17 x 17 6 + c

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