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MHT CET202313 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

If I = 2 x-7 3 x-2 ~d x , then I is given by

Options

  1. A106 27 (3 x-2)^ 3 2 + c , where c is a constant of integration.
  2. B98 27 (3 x-2)^ 3 2 + c , where c is a constant of integration.
  3. C4 27 (3 x-2)^ 3 2 - 34 9 (3 x-2)^ 1 2 + c , where c is a constant of integration.
  4. D4 27 (3 x-2)^ 3 2 + 34 9 (3 x-2)^ 1 2 + c , where c is a constant of integration

Correct answer

C. 4 27 (3 x-2)^ 3 2 - 34 9 (3 x-2)^ 1 2 + c , where c is a constant of integration.

Step-by-step solution

aligned I & = 2 x-7 3 x-2 ~d x & = 2 3 (3 x-2)- 17 3 3 x-2 ~d x & = 2 3 (3 x-2)^ 1 2 ~d x- 17 3 (3 x-2)^ -1 2 ~d x & = 2 3 (3 x-2)^ 3 2 3 2 1 3 - 17 3 (3 x-2)^ 1 2 1 2 1 3 + c & = 4 27 (3 x-2)^ 3 2 - 34 9 (3 x-2)^ 1 2 + c aligned

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